Guotao Wang

• PhD
• Full Professor at Shanxi Normal University

This paper focuses on radial p-k-convex solutions for the following p-k-Hessian equation where \(p\ge 2\), \(k\in \{1,2,...,n\}\), \(E\subset \mathbb {R}^{n}(n\ge 2)\) denotes a ball. For the case of \(0<m<(p-1)k\), \(\mu =0\), the multiplicity of radial p-k-convex solutions of the above p-k-Hessian equation is established by the sub-supersolutions...

In this article, we first introduce a new fractional g g -Laplacian Monge-Ampère operator: F g s v ( x ) ≔ inf P.V. ∫ R n g v ( z ) − v ( x ) ∣ C − 1 ( z − x ) ∣ s d z ∣ C − 1 ( z − x ) ∣ n + s ∣ C ∈ C , {F}_{g}^{s}v\left(x):= \inf \left\{\hspace{0.1em}\text{P.V.}\hspace{0.1em}\mathop{\int }\limits_{{{\mathbb{R}}}^{n}}g\left(\frac{v\left(z)-v\left(...

In this paper, we study a class of coupled fractional conformable Langevin differential system and inclusion on the circular graph. On the one hand, the existence and uniqueness of solutions of this coupled fractional conformable Langevin differential system are studied by fixed point theorems. On the other hand, in the multivalued case, the existe...

In this paper, we study a class of coupled fractional conformable Langevin differential system and inclusion on the circular graph. On the one hand, the existence and uniqueness of solutions of this coupled fractional conformable Langevin differential system are studied by fixed point theorems. On the other hand, in the multivalued case, the existe...

This study first establishes several maximum and minimum principles involving the nonlocal Monge-Ampère operator and the multi-term time-space fractional Caputo-Fabrizio derivative. Based on the maximum principle established above, on the one hand, we show that a family of multi-term time-space fractional parabolic Monge-Ampère equations has at mos...

In this work, we consider a class of fuzzy fractional delay integro-differential equations with the generalized Caputo-type Atangana-Baleanu (ABC) fractional derivative. By using the monotone iterative method, we not only obtain the existence and uniqueness of the solution for the given problem with the initial condition but also give the monotone...

Disilane is an important inorganic compound, which is widely used in many fields. This study first focuses on investigating the existence and uniqueness of solutions to fractional conformable coupled boundary value problem with the p-Laplacian operator on the disilane graph. The fixed point theorem is used to analyze these results. Additionally, th...

The study is being applied to a model involving silane and on cyclopentasilane graph. We consider a graph with labeled vertices by 0 or 1 inspired by the molecular structure of cyclopentasilane. In this paper, we first study the existence of solutions to fractional conformable boundary value problem on the cyclopentasilane graph by applying Scheafe...

Fermentation is an indispensable link in wine brewing, and mathematical modeling is an effective means to study fermentation process, which can reveal the characteristics of state variables and help to optimize the control of fermentation process. In this paper, a new model with fractional derivative of the wine fermentation is proposed. The basic...

This article combines (k,Θ)-Hilfer fractional calculus with glucose molecular graph, defines fractional differential and inclusion systems on each edge of a glucose molecular graph by the assumption that 0 or 1 marks the vertices, and studies the single-valued and multi-valued (k,Θ)-Hilfer type fractional boundary value problems on the glucose mole...

This paper studies the following coupled k-Hessian system with different order fractional Laplacian operators: Firstly, we discuss decay at infinity principle and narrow region principle for the k-Hessian system involving fractional order Laplacian operators. Then, by exploiting the direct method of moving planes, the radial symmetry and monotonici...

The present study examines the Langevin coupled boundary value problem with the fractional conformable derivative on the ethane graph. The main objective of this research is to establish the existence and uniqueness of solutions with the help of the fixed point theorem and to analyze the Ulam stability of the corresponding problem. Several examples...

In this article, a numerical method based on Chelyshkov operation matrix is built to investigate a time-space fractional reaction diffusion model. First of all, we transform the solution of time-space fractional reaction diffusion equation into the solution of a linear system by using operational matrix method. Next, in order to validate the accura...

In this content, we investigate a class of fractional parabolic equation with general nonlinearities $$\begin{aligned} \frac{\partial z(x,t)}{\partial t}-(\Delta +\lambda )^{\frac{\beta }{2}}z(x,t)=a(x_{1})f(z), \end{aligned}$$ ∂ z ( x , t ) ∂ t - ( Δ + λ ) β 2 z ( x , t ) = a ( x 1 ) f ( z ) , where a and f are nondecreasing functions. We first pr...

Gronwall–Bellman-type inequalities provide a very effective way to investigate the qualitative and quantitative properties of solutions of nonlinear integral and differential equations. In recent years, local fractional calculus has attracted the attention of many researchers. In this paper, based on the basic knowledge of local fractional calculus...

This paper introduces a new concept of Caputo type interval-valued fractional conformable calculus. Based on this, some theorems and properties related to fractional conformable calculus are presented. As an application, this paper attempts to investigate an initial value problem of functional integro-differential equations with Caputo type interva...

We study parabolic equation with the tempered fractional Laplacian and logarithmic nonlinearity by the direct method of moving planes. We first prove several important theorems, such as asymptotic maximum principle, asymptotic narrow region principle and asymptotic strong maximum principle for antisymmetric functions, which are critical factors in...

This paper studies the existence of extremal solutions for a nonlinear boundary value problem of Bagley–Torvik differential equations involving the Caputo–Fabrizio-type fractional differential operator with a non-singular kernel. With the help of a new inequality with a Caputo–Fabrizio fractional differential operator, the main result is obtained b...

This paper investigates the positive radial solutions of a nonlinear k -Hessian system. Λ S k 1 / k λ D 2 z 1 S k 1 / k λ D 2 z 1 = b x φ z 1 , z 2 , x ∈ ℝ N Λ S k 1 / k λ D 2 z 2 S k 1 / k λ D 2 z 2 = h x ψ z 1 , z 2 , x ∈ ℝ N , where Λ is a nonlinear operator and b , h , φ , ψ are continuous functions. With the help of Keller–Osserman type condit...

By developing the direct method of moving planes, we study the radial symmetry of nonnegative solutions for a fractional Laplacian system with different negative powers: (−Δ)α2u(x)+u−γ(x)+v−q(x)=0,x∈RN, (−Δ)β2v(x)+v−σ(x)+u−p(x)=0,x∈RN, u(x)≳|x|a,v(x)≳|x|bas|x|→∞, where α,β∈(0,2), and a,b>0 are constants. We study the decay at infinity and narrow re...

In this paper, we investigate a class of nonlinear Schrödinger systems containing a nonlinear operator under Osgood-type conditions. By employing the iterative technique, the existence conditions for entire positive radial solutions of the above problem are given under the cases where components μ and ν are bounded, μ and ν are blow-up, and one of...

In this paper, we consider a coupled k-Hessian system Sk(D2u)−λ1um+vp+f(u,v)=0inΩ,Sk(D2v)−λ2vn+uq+g(u,v)=0inΩ,where Ω⊂RN is a ball, Sk(D2u) stands for k-Hessian operator. By applying the linearization technology and the implicit function theorem, we state and certify the non-degeneracy and uniqueness of the positive radial solutions to a coupled k-...

In this paper, we are concerned with the existence of the positive bounded and blow-up radial solutions of the (k1, k2)-Hessian system {G(K11k1)K11k1=b1(|x∣)g1(z1,z2),x∈ℝN,G(K21k2)K21k2=b2(|x|)g2(z1,z2),x∈ℝN, where G is a nonlinear operator, Ki=Ski(λ(D2zi))+ψi(|x|)|∇zi|ki,i=1,2. Under the appropriate conditions on g1 and g2, our main results are ob...

The aim of this paper is to deal with the existence of extremal solutions for a novel class of nonlinear fractional p-Laplacian differential equation in terms of-Caputo fractional derivative equipped with a new class of nonlinear boundary conditions. Initially, we focus on the linear problem and we give an explicit form of the solutions, from which...

In this paper, we consider the following generalized nonlinear k-Hessian system $$\left\{ {\matrix{{{\cal G}\left( {S_k^{{1 \over k}}(\lambda ({D^2}{z_1}))} \right)S_k^{{1 \over k}}(\lambda ({D^2}{z_1})) = \varphi (\left| x \right|,{z_1},{z_2}),\,\,\,x \in {\mathbb{R}^N},} \cr {{\cal G}\left( {S_k^{{1 \over k}}(\lambda ({D^2}{z_2}))} \right)S_k^{{1...

In this paper, we consider two kinds of nonlinear Schrödinger equations with the fractional Laplacian and Hardy potential (λ|x|s, 0<λ⩽λ∗,λ∗ is a constant of the Hardy-Sobolev inequality), which represent the generalized form of Hartree and Pekar-Choquard type time dependent fractional Hardy-Schrödinger equations. Applying the direct method of movin...

In this paper, the authors study a initial boundary value problems (IBVP) for space-time fractional conformable partial differential equation (PDE). Several inequalities of fractional conformable derivatives at extremum points are presented and proved. Based on these inequalities at extremum points, a new maximum principle for the space-time fracti...

This paper considers the initial boundary value problem for the time-space fractional delayed diffusion equation with fractional Laplacian. By using the semigroup theory of operators and the monotone iterative technique, the existence and uniqueness of mild solutions for the abstract time-space evolution equation with delay under some quasimonotone...

This paper first introduces a generalized fractional p-Laplacian operator (–Δ)sF;p. By using the direct method of moving planes, with the help of two lemmas, namely decay at infinity and narrow region principle involving the generalized fractional p-Laplacian, we study the monotonicity and radial symmetry of positive solutions of a generalized frac...

In this paper, the authors consider a IBVP for the time-space fractional PDE with the fractional conformable derivative and the fractional Laplace operator. A fractional conformable extremum principle is presented and proved. Based on the extremum principle, a maximum principle for the fractional conformable Laplace system is established. Furthermo...

This paper considers a class of Schrödinger elliptic system involving a nonlinear operator. Firstly, under the simple condition on and ', we prove the existence of the entire positive bounded radial solutions. Secondly, by using the iterative technique and the method of contradiction, we prove the existence and nonexistence of the entire positive b...

In this paper, we investigate the method of moving planes for fractional p-Laplacian system. We firstly discuss the key ingredients for the method of moving planes such as maximum principle for anti-symmetric functions, decay at infinity and boundary estimate. Then we apply the method of moving planes to establish the radial symmetry and the monoto...

In this paper, by applying the direct method of moving planes, the authors study the radial symmetry of standing waves for nonlinear fractional Laplacian Schrödinger systems with Hardy potential. Firstly, under the condition of infinite decay, the radial symmetry of the solution is established. Secondly, under the condition of no decay, the radial...

In this paper, we consider the following nonlinear k-Hessian system {G(Sk1k(λ(D2z1)))Sk1k(λ(D2z1))=b(|x|)φ(z1,z2),x∈RN,G(Sk1k(λ(D2z2)))Sk1k(λ(D2z2))=h(|x|)ψ(z1,z2),x∈RN,where G is a nonlinear operator. This paper first proves the existence of the entire positive bounded radial solutions, and secondly gives the existence and non-existence conditions...

In this paper, we study the extremal solutions of nonlinear fractional p‐Laplacian differential system with the fractional conformable derivative by applying monotone iterative method and a half‐pair of upper and lower solutions. For the smooth running of our work, we develop a comparison principle about linear system, which play a very crucial rol...

Nonlinear fractional differential equation is a very novel subject. This book is a summary of the author's research on nonlinear fractional differential equations for many years. This book includes several types of nonlinear fractional differential equations, fractional integral-differential equations, fractional impulsive differential equations, a...

In this paper, under certain nonlinear growth conditions, we investigate the existence and successive iterations for the unique positive solution of a nonlinear fractional q-integral boundary problem by employing hybrid monotone method, which is a novel approach to nonlinear fractional q-difference equation. This paper not only proves the existence...

The purpose of the current study is to investigate IBVP for spatial‐time fractional differential equation with Hadamard fractional derivative and fractional Laplace operator(−Δ)β. A new Hadamard fractional extremum principle is established. Based on the new result, a Hadamard fractional maximum principle is also proposed. Furthermore, the maximum p...

Abstract This study establishes some new maximum principle which will help to investigate an IBVP for multi-index Hadamard fractional diffusion equation. With the help of the new maximum principle, this paper ensures that the focused multi-index Hadamard fractional diffusion equation possesses at most one classical solution and that the solution de...

By using the monotone iterative method combined with the upper and lower solutions, we not only prove the existence of extremal solutions for the nonlinear fractional Langevin equation involving fractional conformable derivative and non-separated integro-differential strip-multi-point boundary conditions, but also provide two computable explicit mo...

Fractional calculus has gained more attention during the last decade due to their effectiveness and potential applicability in various problems of mathematics and statistics. Several authors have studied the pathway fractional operator representations of various special functions such as Bessel function, generalized Bessel functions, Struve functio...

By using monotone iterative method, the extremal solutions and the unique solution are obtained for a nonlinear fractional p-Laplacian boundary value problem involving fractional conformable derivatives and nonlocal integral boundary conditions. Comparison theorems related to the proposed study are also proved. The paper concludes with an illustrat...

Hadamard fractional calculus theory has made many scholars enthusiastic and excited because of its special logarithmic function integral kernel. In this paper, we focus on a class of Caputo-Hadamard-type fractional turbulent flow model involving p(t)-Laplacian operator and Erdélyi-Kober fractional integral operator. The p(t)-Laplacian operator invo...

In this article, by the use of the lower and upper solutions method, we prove the existence of a positive solution for a Riemann–Liouville fractional boundary value problem. Furthermore, the uniqueness of the positive solution is given. To demonstrate the serviceability of the main results, some examples are presented.

This article studies the generalized Mittag–Leffler stability of Hilfer fractional nonautonomous system by using the Lyapunov direct method. A new Hilfer type fractional comparison principle is also proved. The novelty of this article is the fractional Lyapunov direct method combined with the Hilfer type fractional comparison principle. Finally, ou...

The stability of the zero solution of a class of nonlinear Hadamard type fractional differential system is investigated by utilizing a new fractional comparison principle. The novelty of this paper is based on some new fractional differential inequalities along the given nonlinear Hadamard fractional differential system. A comparison principle empl...

Abstract This paper is devoted to the study of Gronwall–Bellman-type inequalities on an arbitrary time scale T $\mathbb{T}$. We investigate some new explicit bounds of a certain class of nonlinear retarded dynamic inequalities of Gronwall–Bellman type on time scales. These inequalities extend some known dynamic inequalities on time scales. We also...

In this paper, by applying the method of moving planes, we conclude the conclusions for the radial symmetry of standing waves for a nonlinear Schrödinger equation involving the fractional Laplacian and Hardy potential. First, we prove the radial symmetry of solution under the condition of decay near infinity. Based upon that, under the condition of...

Abstract In this article, we first create a new comparison principle for a nonlinear impulsive boundary problem involving different deviating arguments. Then we employ the new result and iterative method to study the existence of the max-minimal solution of a second-order impulsive functional integro-differential equation. The results achieved in t...

This article investigates a new class of boundary value problems of one-dimensional lower-order nonlinear Hadamard fractional differential equations and nonlocal multi-point discrete and Hadamard integral boundary conditions. By using monotone iterative method, we not only seek the twin positive solutions of the problem but also show that the monot...

In this paper, we study the positive solutions of the Schrödinger elliptic system \begin{document}$ \begin{equation*} \begin{split} \left\{\begin{array}{ll}{\operatorname{div}(\mathcal{G}(|\nabla y|^{p-2})\nabla y) = b_{1}(|x|) \psi(y)+h_{1}(|x|) \varphi(z),}& {x \in \mathbb{R}^{n}(n \geq 3)}, \\ {\operatorname{div}(\mathcal{G}(|\nabla z|^{p-2})\na...

In this paper, we investigate radial symmetry and monotonicity of positive solutions to a logarithmic Choquard equation involving a generalized nonlinear tempered fractional \begin{document}$ p $\end{document}-Laplacian operator by applying the direct method of moving planes. We first introduce a new kind of tempered fractional \begin{document}$ p...

In this paper, we concern a Hadamard-type fractional-order turbulent flow model with deviating arguments. By using some standard fixed point theorems, the uniqueness, existence and nonexistence of solutions of the fractional turbulent flow model are investigated. Our results are new and are well illustrated with the aid of three examples.

In this article, a family of nonlinear diffusion equations involving multi-term Caputo-Fabrizio time fractional derivative is investigated. Some maximum principles are obtained. We also demonstrate the application of the obtained results by deriving some estimation for solution to reaction-diffusion equations.

A Hadamard type fractional integro-differential equation on infinite intervals is considered. By using monotone iterative technique, we not only get the existence of positive solutions, but also seek the positive minimal and maximal solutions and get two explicit monotone iterative sequences which converge to the extremal solutions. At last, to ill...

The primary work of this paper is to investigate twin iterative positive solutions of a class of fractional q-difference Schrödinger equations appeared in Li et al. (2015). By employing a completely different approach—monotone iterative approach, this paper not only establishes excellent conditions to ensure the existence of the twin iterative posi...

In this paper, weinvestigate the existence of minimal nonnegative solution for a class of nonlinear fractional integro-differential equations on semi-infinite intervals in Banach spaces by applying the cone theory and the monotone iterative technique. An example is given for the illustration of main results.

In this paper, by employing the lower and upper solutions method, we give an existence theorem for the extremal solutions for a nonlinear impulsive differential equations with multi-orders fractional derivatives and integral boundary conditions. A new comparison result is also established.

This paper is concerned with the existence of solutions for nonlinear fractional differential equations of Volterra type with nonlocal fractional integro-differential boundary conditions on an infinite interval. The results are obtained by using the Altman fixed point theorem. An example is presented in order to illustrate the main results.

This paper investigates the existence of the unique solution for a Hadamard fractional integral boundary value problem of a Hadamard fractional integro-differential equation with the monotone iterative technique. Two examples to illustrate our result are given.

In this paper, our main objective is to establish certain new image formulas of R- and G-functions by applying the operators of fractional derivative involving Appell’s function F3(.) due to Saigo-Maeda and the main results interpreted graphically by implementing the MatLab(R2012a). Furthermore, by employing some integral transforms on the resultin...

By establishing a comparison theorem and applying the monotone iterative technique combined with the method of lower and upper solutions, we investigate the existence of extremal solutions of the initial value problem for fractional q-difference equation involving Caputo derivative. An example is presented to illustrate the main result.

We investigate a nonlinear impulsive qk-integral boundary value problem by means of Leray-Schauder degree theory and contraction mapping principle. The conditions ensuring the existence and uniqueness of solutions for the problem are presented. An illustrative example is discussed.

We discuss the existence and approximation of positive solutions for nonlinear Riemann-Liouville fractional differential equations with nonlocal fractional integro-differential boundary conditions on an unbounded domain by using a monotone iterative procedure. It is shown that the sequences of iterates converge to a unique positive solution of the...

This paper investigates the existence of positive extremal solutions for nonlinear impulsive q k -difference equations via a monotone iterative method. The main result is well illustrated with the aid of an example. MSC: 34B37, 39A13.

In the present paper, we aim to investigate a new q-integral inequality of Gruss type for the Saigo fractional q-integral operator. Some special cases of our main results are also provided. The results presented in this paper improve and extend some recent results.

Abstract This paper studies the existence of extremal solutions for nonlinear fractional differential equations with nonlinear integral boundary conditions and explores an explicit algorithm which converges to the extremal solutions of the problem at hand. An example is discussed for the illustration of the main work.

In this paper, we discuss the existence of solutions for nonlinear q-difference equations with nonlocal q-integral boundary conditions. The first part of the paper deals with some existence and uniqueness results obtained by means of standard tools of fixed point theory. In the second part, sufficient conditions for the existence of extremal soluti...

By employing the monotone iterative technique, we not only establish the existence of the unique solution for a fractional integral boundary value problem on semi-infinite intervals, but also develop an explicit iterative sequence for approximating the solution and give an error estimate for the approximation, which is an important improvement of e...

In this paper, we investigate a nonlinear second order boundary value problem of q-integro-difference equations supplemented with non-separated boundary conditions. Sufficient conditions for the existence and nonexistence of solutions are presented. Examples are provided for explanation of the obtained work.

In this article, some new explicit bounds on solutions to a class of new nonlinear integral inequalities of Gronwall–Bellman–Bihari type with delay for discontinuous functions are established. These inequalities generalize and improve some former famous results about inequalities, and which provide an excellent tool to discuss the qualitative and q...

In this paper, positive solutions of fractional differential equations with nonlinear terms depending on lower-order derivatives on a half-line are investigated. The positive extremal solutions and iterative schemes for approximating them are obtained by applying a monotone iterative method. An example is presented to illustrate the main results.

In this paper, we investigate the existence and uniqueness of solutions for impulsive nonlinear differential equations of fractional order with non local integral boundary condition. Our results are based on some suitable fixed point theorems. An illustrative example is presented.

We first obtain that subdifferentials of set-valued mapping from finite-dimensional spaces to finite-dimensional possess certain relaxed compactness. Then using this weak compactness, we establish gap functions for generalized Stampacchia vector variational-like inequalities which are defined by means of subdifferentials. Finally, an existence resu...

A new impulsive multi-orders fractional differential equation is studied. The existence and uniqueness results are obtained for a nonlinear problem with fractional integral boundary conditions by applying standard fixed point theorems. An example for the illustration of the main result is presented.

In this paper, some new integral inequalities related to the bounded functions, involving Saigo's fractional integral operators, are eshtablished. Special cases of the main results are also pointed out.

A remarkably large number of Grüss type fractional integral inequalities involving the special function have been investigated by many authors. Very recently, Kalla and Rao (Matematiche LXVI(1):57-64, 2011) gave two Grüss type inequalities involving the Saigo fractional integral operator. Using the same technique, in this paper, we establish certai...

By applying an iterative technique, sufficient conditions are obtained for the existence of the unique solution of the nonlinear neutral fractional integro-differential equation involving two Riemann–Liouville derivatives of different fractional orders. Finally, an example is also given to illustrate the availability of our main results.

A monotone iterative method is applied to show the existence of an extremal solution for a nonlinear system involving the right-handed Riemann–Liouville fractional derivative with nonlocal coupled integral boundary conditions. Two comparison results are established. As an application, an example is presented to demonstrate the efficacy of the main...

In this paper, we propose novel hybrid edge and region based active contour models. First, we consider geodesic curve and region-based model, and evolve contours based on global information to segment images with intensity homogeneity. Second, we extend the global model to the local intensity fitting energy for segmenting the images with intensity...

We showthe existence and uniqueness of solutions for an antiperiodic boundary value problem of nonlinear impulsive q(K) difference equations by applying some well-known fixed point theorems. An example is presented to illustrate the main results.

By employing known Guo-Krasnoselskii fixed point theorem, we investigate the eigenvalue interval for the existence and nonexistence of at least one positive solution of nonlinear fractional differential equation with integral boundary conditions.

A nonlinear impulsive integrodifference equation within the frame of q k -quantum calculus is investigated by applying using fixed point theorems. The conditions for existence and uniqueness of solutions are obtained.

In some recent works dealing with the existence of solutions for impulsive fractional differential equations, it is pointed out that the concept of solutions for such equations in some preceding papers is incorrect. In support of this claim, the authors of these papers begin with a counterexample. The objective of this note to indicate the mistake...

This paper investigates the existence of solutions for nonlinear fractional differential equations with integral boundary conditions on an unbounded domain. An example illustrating how the theory can be applied in practice is also included.

By employing the monotone iterative method, this paper not only establishes the existence of the minimal and maximal positive solutions for multipoint fractional boundary value problem on an unbounded domain, but also develops two computable explicit monotone iterative sequences for approximating the two positive solutions. An example is given for...

Applying the monotone iterative method, we investigate the existence of solutions for a coupled system of nonlinear neutral fractional differential equations, which involves Riemann-Liouville derivatives of different fractional orders. As an application, an example is presented to illustrate the main results. (c) 2013 Elsevier Ltd. All rights reser...

By applying an iterative technique, a necessary and sufficient condition is obtained for the existence of the unique solution of nonlinear fractional differential equations involving two Riemann-Liouville derivatives of different fractional orders. Finally, an example is also given to illustrate the availability of our main results.

In this paper, by employing the fixed point theory and the monotone iterative technique, we investigate the existence of a unique solution for a class of nonlinear fractional integro-differential equations on semi-infinite domains in a Banach space. An explicit iterative sequence for approximating the solution of the boundary value problem is deriv...

In this paper, we prove some new fixed point theorems for a mixed monotone mapping under more generalized nonlinear contractive conditions in a metric space endowed with partial order. Our results generalize and improve several results of T. Gnana Bhaskar and V. Lakshmikantham [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 65, No. 7...

In this paper, we consider the existence of positive solutions for a class of nonlinear boundary-value problem of fractional differential equations with integral boundary conditions. Our analysis relies on known Guo-Krasnoselskii fixed point theorem.

This paper investigates the existence of nonnegative solutions for nonlinear fractional differential equations with nonlocal fractional integrodifferential boundary conditions on an unbounded domain by means of Leray-Schauder nonlinear alternative theorem. An example is discussed for the illustration of the main work.

By using the fixed point index theory, this paper investigates the existence of multiple positive solutions to a three-point boundary value problem for nonlinear fractional-order differential equation with an advanced argument.