Sadarangani Kishin

• University of Las Palmas de Gran Canaria

We consider a generalization of a functional equation that models the learning process in various animal species. The equation can be considered nonlocal, as it is built with a convex combination of the unknown function evaluated at mixed arguments. This makes the equation contain two terms with vanishing delays. We prove the existence and uniquene...

We consider a nonlocal functional equation that is a generalization of the mathematical model used in behavioral sciences. The equation is built upon an operator that introduces a convex combination and a nonlinear mixing of the function arguments. We show that, provided some growth conditions of the coefficients, there exists a unique solution in...

In this paper, we examine the solvability of a functional equation in a Lipschitz space. As an application, we use our result to determine the existence and uniqueness of solutions to an equation describing a specific type of choice behavior model for the learning process of the paradise fish. Finally, we present some concrete examples where, using...

We present some remarks on [Carpathian J. Math. 39 (2023), No 2, 541--551] in order to obtain a unique non trivial solution.

We study the existence of positive solutions for a fractional differential equation with integral boundary conditions. Our solutions are placed in the space of Hölder functions and the main tools used in the proof of the results are the classical Schauder fixed point theorem and a sufficient condition about the relative compactness in Hölder spaces...

In the present paper, by using the mixed monotone operator method we prove the existence and uniqueness of positive solution to the following cantilever-type boundary value problem u(4)(t)=f(t,u(t),u(αt))+g(t,u(t)),0<t<1,α∈(0,1),u(0)=u′(0)=u′′(1)=u′′′(1)=0.\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts}...

In this paper, we are interested in the study of the existence and uniqueness of positive solutions to the nonlinear singular fractional differential equation \(D^{\alpha }_{0^+} u(t)+f(t,u(t),(Hu)(t))=0\) with \(0<t<1\), where \(D^{\alpha }_{0^+}\) denotes the classical Riemmann Liouville derivative, under the integral boundary conditions \(u(0)=u...

From a fixed point theorists’ view, Hutchinson considered a fractal set as a fixed point problem and applied the Banach contraction principle to prove its existence. In this paper, we present a result about the existence of fractal for a finite iterated condensing function using the degree of nondensifiability.

We introduce the class of enriched φ-contractions in Banach spaces as a natural generalization of φ-contractions and study the existence and approximation of the fixed points of mappings in this new class, which is shown to be an unsaturated class of mappings in the setting of a Banach space. We illustrated the usefulness of our fixed point results...

In this article, we discuss the solvability of infinite systems of singular integral equations of two variables in the Banach sequence spaces C(I ? I, ?p) with I = [0, T], T > 0 and 1 < p < ? with the help of Meir-Keeler condensing operators and Hausdorff measure of noncompactness. With an example, we illustrate our findings.

In this paper, we study the existence of positive solutions for the following nonlinear fractional boundary value problem: $$\begin{aligned} \left. \begin{array}{ll}D^{\alpha }_{0^+} u(t)+f(t,u(t),(Hu)(t))=0,&{} 0<t<1,\\ u(0)=u'(0)=0,\ \ u'(1)=\beta u(\xi ), \end{array} \right\} \end{aligned}$$where \(2<\alpha \le 3\), \(0<\xi < 1\), \(0\le \beta \...

In this paper, we present a result about the existence and uniqueness of positive solutions for a class of singular fractional differential equations with infinite-point boundary value conditions. The main tool used in the proof of the results is a fixed point theorem.

The purpose of this paper is to study the existence of positive solutions to a class of fractional differential equations with infinite-point boundary value conditions. Our solutions are placed in the space of Lipschitz functions and the main tools used in the proof of the results are a sufficient condition about the relative compactness in Holder...

In this work, we discuss the existence and uniqueness of positive solutions for the second order integral boundary value problem \left\{ \begin{aligned} x''(t) + f(t,x(t),(Hx)(t)) &=0, \quad 0 < t < 1,\\ x(0)=0,\quad x(1)&= \int_{0}^{1}a(s)x(s)ds, \end{aligned} \right. where the function f has a singularity at t_{0}=0 . Our main tool is a fixed poi...

In this article, we present a sufficient condition about the length of the interval for the existence and uniqueness of mild solutions to a fractional boundary value problem with Sturm-Liouville boundary conditions when the data function is of Lipschitzian type. Moreover, we present an application of our result to the eigenvalues problem and its co...

In this paper, we focus on an integral equation which allows us to model the dynamics of the capillary rise of a fluid inside a tubular column. Using Schauder's fixed-point theorem, we prove that such integral equation has at least one solution in the Hölder space H1[0,b], where b>0. Moreover, we are able to prove the uniqueness of the solution und...

In this paper, we present a sufficient condition for the uniqueness of solutions to a nonlocal fractional boundaryvalue problem which can be considered as the fractional version to the thermostat model. As application of ourresult, we study the eigenvalues problem associated and, moreover, we get a Lyapunov-type inequality.

In this paper, we prove a fixed point theorem for operators of Meir–Keeler type by using the concept of degree of nondensifiability. As an application of our result, we study the existence of solutions for a class of functional equations appearing in dynamic programming.

Abstract In this paper, we derive some Hartman–Wintner type inequalities for a certain higher order fractional boundary value problem. As an application of our results, we obtain a lower bound for the eigenvalues of the corresponding fractional operator.

In this paper, by using a recent fixed point theorem, we study the existence and uniqueness of positive solutions for the following m-point fractional boundary value problem on an infinite interval $$\begin{aligned} \left\{ \begin{array}{ll} D_{0^{+}}^{\alpha }x(t)+f(t,x(t))=0,&{}\quad 0<t<\infty ,\\ x(0)=x'(0)=0,&{}\quad D_{0^{+}}^{\alpha -1}x(+\i...

In this paper, we study the existence of positive solutions for a nonlocal fractional boundary value problem which can be considered as the fractional analog of the thermostat model. Our solutions are placed in the space of Hölder functions and the main tools used in the proof of the results are a sufficient condition about the relative compactness...

In this paper, we present a Lyapunov type inequality for a nonlinear fractional hybrid boundary value problem. We illustrate the main result through a series of examples.

In this paper, Lyapunov‐type inequalities are derived for a class of fractional boundary value problems with integral boundary conditions. As an application, we obtain a lower bound for the eigenvalues of corresponding equations.

In this paper, we introduce the notion of generalized coupled fixed points and, as a consequence of Darbo’s fixed point theorem associated to an abstract measure of noncompactness, we present a result about the existence of this class of coupled fixed points in Banach spaces. As an application, we investigate the existence of solutions for a class...

In this paper, we prove the existence and uniqueness of solutions for the following fractional boundary value problem $$\begin{aligned} \left\{ \begin{aligned}&^cD_{0+}^\alpha u(t)=\lambda f(t,u(t)),\quad t\in [0,1],\\&u(0)=\gamma I_{0+}^\rho u(\eta )=\gamma \int _0^\eta \frac{(\eta -s)^{\rho -1}}{\Gamma (\rho )}u(s)\mathrm {d}s, \end{aligned} \rig...

In this paper the authors study a fractional quadratic integral equation of Urysohn-Volterra type. They show that the integral equation has at least one monotonic solution in the Banach space of all real functions defined and continuous on the interval [0, 1]. The main tools in the proof are a fixed point theorem due to Darbo and a monotonicity mea...

In the present work, we discuss the existence of a unique positive solution of a boundary value problem for nonlinear fractional order equation with singularity. Precisely, order of equation $D_{0+}^\alpha u(t)=f(t,u(t))$ belongs to $(3,4]$ and $f$ has a singularity at $t=0$ and as a boundary conditions we use $u(0)=u(1)=u'(0)=u'(1)=0$. Using fixed...

We investigate a q-fractional integral equation with supremum and prove an existence theorem for it. We will prove that our q-integral equation has a solution in C[0, 1] which is monotonic on [0, 1]. The monotonicity measure of noncompactness due to Banas and Olszowy and Darbo’s theorem are the main tools used in the proof our main result.

In this paper, we study the existence of positive solutions for a class of nonlinear fractional boundary value problems with integral boundary conditions in Hölder spaces. Our analysis relies on a sufficient condition for the relative compactness in Hölder spaces and the classical Schauder fixed point theorem.

In this paper, we use the mixed monotone operator method to study the following nonlinear boundary value problem $$\begin{aligned} \left\{ \begin{array}{ll} -u'''(t)=f(t,u(t),u(\varrho t))+g(t,u(t)),&{}\quad 0<t<1,\,\varrho \in (0,1), \\ u(0)=u''(0)=u(1)=0. \end{array} \right. \end{aligned}$$An example is provided to illustrate the results.

In this paper, we study sufficient conditions for the existence of positive solutions to a class of fractional differential equations of arbitrary order. Our solutions are placed in the space of Lipschitz functions and, perhaps, this is a part of the originality of the paper. For our study, we use a recent result about the relative compactness in H...

In this paper, we use a mixed monotone operator method to investigate the existence and uniqueness of positive solution to a nonlinear fourth-order boundary value problem which describes the deflection of an elastic beam with the left extreme fixed and the right extreme is attached to a bearing device given by a known function. Moreover, we present...

The principal aim of this chapter is to consider the function space consisting of functions defined on a compact metric space with growths tempered by a given modulus of continuity and its connection with the measures of noncompactness. The chapter is inspired in the papers [1, 2].

The main purpose of this paper is to establish some new results about the existence and uniqueness for coincidence problems for two single-valued mappings. Moreover, we present some applications of our results to the existence and uniqueness of solutions of some boundary value problems.

In this paper, we prove a best proximity point theorem for generalized weak contractions with discontinuous control functions in the context of metric spaces and partially ordered metric spaces. The main argument in our proofs is based on transforming a question of best proximity point to one about a fixed point. Moreover, we will use a weaker cond...

In this paper, we present some Lyapunov-type inequalities for a nonlinear fractional heat equation with nonlocal boundary conditions depending on a positive parameter. As an application, we obtain a lower bound for the eigenvalues of corresponding equations.

The main aim of this paper is to present some theorems in order to guarantee existence and uniqueness of best proximity points under rational contractivity conditions using very general test functions. To illustrate the variety of possible test functions, we include some examples of pairs of functions which are included in innovative papers publish...

An existence and uniqueness of solution of local boundary value problem with discontinuous matching condition for the loaded parabolic-hyperbolic equation involving the Caputo fractional derivative and Riemann-Liouville integrals have been investigated. The uniqueness of solution is proved by the method of integral energy and the existence is prove...

In this paper, new Lyapunov-type inequalities are obtained for the case when one is dealing with a class of fractional two-point boundary value problems. As an application of this result, we obtain a lower bound for the eigenvalues of corresponding equations. Copyright

We introduce the concept of cone measure of noncompactness and obtain some generalizations of Darbo’s theorem via this new concept. As an application, we establish an existence theorem for a system of integral equations. An example is also provided to illustrate the obtained result.

In this work, we investigate a linear differential equation involving Caputo-Fabrizio fractional derivative of order $1<\beta\leq 2$. Under some assumptions the considered equation is reduced to an integer order differential equation and solutions for different cases are obtained in explicit forms. We also prove a uniqueness of a solution of an ini...

This research work is devoted to investigations of the existence and uniqueness of the solution of a non-local boundary value problem with discontinuous matching condition for the loaded equation. Considering parabolic-hyperbolic type equations involves the Caputo fractional derivative and loaded part joins in Riemann-Liouville integrals. The uniqu...

In the Banach space of real functions which are defined, bounded and continuous on an unbounded interval, we study the solvability of a perturbed Erdélyi–Kober fractional quadratic integral equation.

In the Banach space of real functions which are defined, bounded and continuous on an unbounded interval, we study the solvability of a perturbed Erdélyi–Kober fractional quadratic integral equation.

In this work, we study the existence and uniqueness of solutions to non-local boundary value problems with integral gluing condition. Mixed type equations (parabolic-hyperbolic) involving the Caputo fractional derivative have loaded parts in Riemann-Liouville integrals. Thus we use the method of integral energy to prove uniqueness, and the method o...

The main purpose of this paper is to study the existence of solutions for the following hybrid nonlinear fractional pantograph equation $$ \left\{ \begin{aligned} &D_{0+}^\alpha \left[\frac{x(t)}{f(t,x(t),x(\varphi(t)))}\right]=g(t,x(t),x(\rho(t))),\,\,0<t<1\\ &x(0)=0, \end{aligned} \right. $$ where $\alpha\in (0,1)$, $\varphi$ and $\rho$ are funct...

In this work, we investigate a linear differential equation involving Caputo-Fabrizio fractional derivative of order $1<\beta\leq 2$. Under some assumptions the considered equation is reduced to an integer order differential equation and solutions for different cases are obtained in explicit forms. We also prove a uniqueness of a solution of an ini...

In this paper, we establish new Hartman–Wintner-type inequalities for a class of nonlocal fractional boundary value problems. As an application, we obtain a lower bound for the eigenvalues of corresponding equations. Copyright © 2016 John Wiley & Sons, Ltd.

In this work, we investigate a linear differential equation involving Caputo-Fabrizio fractional derivative of order 1 < β ≤ 2. Under some assumptions the considered equation is reduced to an integer order differential equation and solutions for different cases are obtained in explicit forms. We also prove a uniqueness of a solution of an initial v...

In this paper, we present a result about the existence of a generalized coupled fixed point in the space C[0; 1]. Moreover, as an application of the result, we study the problem of existence and uniqueness of solution in C[0; 1] for a general system of nonlinear functional-integral equations with maximum.

We present some fixed point theorems for contractions of rational type. These theorems generalize some other results appearing in the literature. Moreover, we present some examples illustrating our results. Finally, we present an application to the study of the existence and uniqueness of solutions to a class of functional equations arising in dyna...

In this paper, we introduce the definition of generalized coupled fixed point in the space of the bounded functions on a set S and we prove a result about the existence and uniqueness of such points. As an application of our result, we study the problem of existence and uniqueness of solutions for a class of systems of functional equations which ap...

In this article we first discuss the existence and uniqueness of a solution for the coincidence problem: Find p ∈ X such that Tp = Sp, where X is a nonempty set, Y is a complete metric space, and T, S:X → Y are two mappings satisfying a Wardowski type condition of contractivity. Later on, we will state the convergence of the Picard-Juncgk iteration...

In this paper, we study the existence of the hybrid fractional pantograph equation $$ \left\{\begin{array}{lll} D_{0^+}^{\alpha}\Big[\dfrac{x(t)}{f(t,x(t),x(\mu t))}\Big]=g\big(t,x(t),x(\sigma t)\big),\;0

We introduce Erdélyi-Kober fractional quadratic integral equation with supremum, namely . This equation contains as special cases numerous integral equations studied by other authors. We show that there exists at least one monotonic solution belonging to C[0, 1] of our equation. The main tools in our analysis are Darbo fixed point theorem and the m...

The guest editors of this special issue would like to express their gratitude to the authors of all papers submitted for consideration.

A technique associated with measures of weak noncompactness and measures of noncompactness in strong sense is used to prove an existence result for a functional integral equation with Carath,odory perturbed. Our investigations take place in the space , . An example is also discussed to indicate the natural realizations of our abstract result.

The main purpose of this paper is to present a best proximity point theorem. The novelty of the result is that assumption relative to the contractivity condition is only satisfied by elements verifying a certain condition.

In this paper, we prove the existence and uniqueness of solutions for a coupled system of fractional differential equations with integral boundary conditions. Our analysis relies on a generalized coupled fixed point theorem in the space of the continuous functions defined on [0,1]. An example is also presented to illustrate the obtained results.

In recent times, many authors proved several coupled, tripled, quadrupled and, in general, multidimensional fixed point theorems. In many cases, these results become to be simple consequences of their corresponding unidimensional theorems. In this paper, we show how the weak P-property can be induced in product spaces and how to use it to enunciate...

In this paper, we present a result about the existence of a generalized coupled fixed point in the space C[0; 1]. Moreover, as an application of the result, we study the problem of existence and uniqueness of solution in C[0; 1] for a general system of nonlinear functional-integral equations with maximum.

We study the solvability of a functional-integral equation with deviating arguments, where our investigations take place in the space of Lebesgue integrable functions on an unbounded interval. In this space, we show that our functional-integral equation has at least one nonnegative and nonincreasing solution. The proof of our main result is based o...

The purpose of this paper is provide sufficient conditions for the existence of a unique best proximity point for contractions of Geraghty type. Our paper improves a recent result due to Caballero et al. (Fixed Point Theory and Applications. doi:10.1186/1687-1812-2012-231, 2012).

We introduce the definition of α-coupled fixed point in the space of the bounded functions on a set S and we present a result about the existence and uniqueness of such points. Moreover, as an application of our result, we study the problem of existence and uniqueness of solutions for a class of systems of functional equations arising in dynamic pr...

Using the technique of measures of noncompactness and, in particular, a consequence of Sadovskii’s fixed point theorem, we prove a theorem about the existence and asymptotic stability of solutions of a functional integral equation. Moreover, in order to illustrate our results, we include one example and compare our results with those obtained in ot...

We study an existence result for the following coupled system of nonlinear fractional hybrid differential equations with homogeneous boundary conditions D 0 + α [ x ( t ) / f ( t , x ( t ) , y ( t ) ) ] = g ( t , x ( t ) , y ( t ) ) , D 0 + α y ( t ) / f ( t , y ( t ) , x ( t ) ) = g ( t , y ( t ) , x ( t ) ) , 0 < t < 1 , and x ( 0...

In this paper, we study the existence of solutions for a nonlinear Erdélyi–Kober fractional quadratic integral equations with linear modification of the argument. The main tool used in our considerations is the technique associated to measures of noncompactness. We compare our results with the ones obtained in recent papers. Finally, we present som...

We prove the existence of the PPF dependent fixed point in the Razumikhin class for contractions of rational type in Banach spaces, by using a general class of pairs of functions. Our result has as particular cases a great number of interesting consequences which extend and generalize some results appearing in the literature.

We study the existence of solutions for the following fractional hybrid boundary value problem where 1< α≤ 2 and D α 0+ denotes the Riemann-Liouville fractional derivative. The main tool is our study is the technique of measures of noncompactness in the Banach algebras. Some examples are presented to illustrate our results. Finally, we compare the...

In the present paper, we give some fixed point results for generalized Ćirić type strong almost contractions on partial metric spaces which generalizes some recent results appearing in the literature. Particularly, our result has as a particular case, mappings satisfying a general contractive condition of integral type.

In this article, we prove the existence of solutions of a quadratic integral equation of Fredholm type with a modified argument, in the space of functions satisfying a Hölder condition. Our main tool is the classical Schauder fixed point theorem.

In the very recent paper of Akbar and Gabeleh (2013), by using the notion of P -property, it was proved that some late results about the existence and uniqueness of best proximity points can be obtained from the versions of associated existing results in the fixed point theory. Along the same line, in this paper, we prove that these results can b...

In this article, we prove the existence of solutions of a quadratic integral equation of Fredholm type with a modified argument, in the space of functions satisfying a Holder condition. Our main tool is the classical Schauder fixed point theorem.

Recently, Samet and Vetro proved a fixed point theorem for mappings satisfying a general contractive condition of integral type in orbitally complete metric spaces (Samet and Vetro, Chaos Solitons Fractals 44:1075–1079, 2011). Our aim in this paper is to present a version of the results obtained in the above mentioned paper in the context of ordere...

The purpose of this paper is to provide sufficient conditions for the existence of a unique best proximity point for generalized weakly contractive mappings in the context of complete metric spaces.

We define the quasi-gamma functions as the functions f :]0, infinity[->]0, infinity[ such that f(1) = 1, f(x + 1) = x f(x) for every x > 0, and f is quasi-convex. The main example of quasi-gamma function is the gamma function defined by Euler. We study some properties of the quasi-gamma functions and of the class Q of these functions.

In this paper, we introduce the notion of Geraghty-contractions and consider the related best proximity point in the context of a metric space. We state an example to illustrate our result. MSC: 47H10, 54H25, 46J10, 46J15.

The purpose of this paper is to present a fixed point theorem for cyclic weak contractions in compact metric spaces.

The purpose of this paper is to present a fixed point theorem due to Dass and Gupta (Indian J Pure Appl Math 6:1455–1458, 1975) in the context of partially ordered metric spaces.

In this paper, we study the existence of solutions for the following fractional hybrid initial value problem with supremum {D-0+(alpha) [x(t)/f(t,x(t),max(0 <=tau <=tau)vertical bar x(tau)vertical bar)]= g(t, x(t)), 0 < t < 1, x(0) = 0, where 0 < alpha <= 1 and D-0+(alpha) denotes the Riemann-Liouville fractional derivative. The main tool in our st...

In the present paper, we introduce generalized Geraghty (Proc Am Math Soc 40:604–608, 1973) mappings on partial metric spaces and give a fixed point theorem which generalizes some recent results appearing in the literature.

In this paper, we present a Markov-type inequality for seminormed fuzzy integrals and its connections with Chebyshev’s inequality and other fundamental properties of the classical integral.

We establish that the spectral multiplier $\frak{M}(G_{\alpha})$ associated to the differential operator $$ G_{\alpha}=- \Delta_x +\sum_{j=1}^m{{\alpha_j^2-1/4}\over{x_j^2}}-|x|^2 \Delta_y \; \text{on} (0,\infty)^m \times \R^n,$$ which we denominate Bessel-Grushin operator, is of weak type $(1,1)$ provided that $\frak{M}$ is in a suitable local Sob...

We prove an existence theorem for a quadratic Abel integral equation of the second kind with supremum in the kernel. The quadratic integral equation studied below contains as a special case numerous integral equations encountered in the theory of radiative transfer and in the kinetic theory of gases. We show that the singular quadratic integral equ...

The guest editors of this special issue would like to express their gratitude to the authors who have submitted papers for consideration. We believe that the results presented in this issue will be a source of inspiration for researchers working in nonlinear analysis and related areas of mathematics.

We discuss some existence results for various types of functional, differential, and integral equations which can be obtained with the help of argumentations based on compactness conditions. We restrict ourselves to some classical compactness conditions appearing in fixed point theorems due to Schauder, Krasnosel’skii-Burton, and Schaefer. We prese...

The notion of coupled fixed point is introduced in by Bhaskar and Lakshmikantham in [2]. Very recently, the concept of the tripled fixed point is introduced by Berinde and Borcut [1]. They also proved some triple fixed point theorems. In this manuscript, by using the weak (ψ-φ)-contraction, the results of Berinde and Borcut [1] are generalized.