Weerawat Sudsutad

Ramkhamhaeng University | RU · Department of Statistics

The initial value problem in Cauchy-type under the (k, ψ)-Caputo proportional fractional operators was our focus in this paper. An extended Gronwall inequality and its properties were analyzed. The existence and uniqueness results were proven utilizing the fixed point theory of Banach's and Leray-Schauder's types. The qualitative analysis included...

The ability to accurately predict urban traffic flows is crucial for optimising city operations. Consequently, various methods for forecasting urban traffic have been developed, focusing on analysing historical data to understand complex mobility patterns. Deep learning techniques, such as graph neural networks (GNNs), are popular for their ability...

This paper establishes a novel generalized Gronwall inequality concerning the ψ-Hilfer proportional fractional operators. Before proving the main results, the solution of the linear nonlocal coupled ψ-Hilfer proportional Cauchy-type system with constant coefficients under the Mittag-Leffler kernel is created. The uniqueness result for the proposed...

In this work, we introduce a novel idea of generalized (k,ψ)-Hilfer proportional fractional operators. The proposed operator combines the (k,ψ)-Riemann–Liouville and (k,ψ)-Caputo proportional fractional operators. Some properties and auxiliary results of the proposed operators are investigated. The ψ-Laplace transform and its properties of the prop...

This paper investigates the existence and uniqueness of solutions for a class of nonlinear impulsive fractional pantograph integro–differential equations with multi-point integral boundary conditions in the context of the (\rho_{k},\psi_{k})-Hilfer fractional operator. We transform our problem into an equivalent integral equation, and the uniquenes...

In this paper, we developed a nonlinear mathematical model for the transmission of the monkeypox virus among populations of humans and rodents under the fractal-fractional operators in the context of Atangana-Baleanu. For the theoretical analysis, the renowned theorems of fixed points, like Banach's and Krasnoselskii's types, were used to prove the...

This paper investigates a class of nonlinear impulsive fractional integro-differential equations with mixed nonlocal boundary conditions (multi-point and multi-term) that involves (ρ k , ψ k)-Hilfer fractional derivative. The main objective is to prove the existence and uniqueness of the solution for the considered problem by means of fixed point t...

In this paper, we investigate the existence result for $ (k, \psi) $-Riemann-Liouville fractional differential equations via nonlocal conditions on unbounded domain. The main result is proved by applying a fixed-point theorem for Meir-Keeler condensing operators with a measure of noncompactness. Finally, two numerical examples are also demonstrated...

In this work, radial basis function collocation method (RBFCM) is implemented for generalized time fractional Gardner equation (GTFGE). The RBFCM is meshless and easy-to-implement in complex geometries and higher dimensions, therefore, it is highly demanding. In this work, the Caputo derivative of fractional order ξ ∈ (0, 1] is used to approximate...

In this article, approximate solutions of some PDE of fractional order are investi­gated with the help of a new semi-analytical method called the optimal auxiliary function method. The proposed method was tested upon the time-fractional Fisher equation, the time-fractional Fornberg-Whitham equation, and the time-fractional Inviscid Burger equation....

In this work, numerical solution of multi term space fractional PDE is calculated by using radial basis functions. The fractional derivatives of radial basis functions are evaluated by Caputo and Riemann-Liouville definitions. Local radial basis functions are applied to get stable and accurate solution the problem. Accuracy of the method is assesse...

In the present article, the fractional order differential difference equation is solved by using the residual power series method. Residual power series method solutions for classical and fractional order are obtained in a series form showing good accuracy of the method. Illustrative models are considered to affirm the legitimacy of the technique....

A Haar wavelet collocation method (HWCM) is presented for the solution of Riccati equation subject to the two-point and integral boundary condition. The qua­silinearization technique is applied to linearized the Riccati equation and then the linearized equation with boundary condition is solved by converting into system of algebraic equation with t...

In this paper, we propose a generalized Gronwall inequality in the context of the ψ-Hilfer proportional fractional derivative. Using Picard’s successive approximation and the definition of Mittag–Leffler functions, we construct the representation formula of the solution for the ψ-Hilfer proportional fractional differential equation with constant co...

The aim of the paper is to present an analysis of special random impulsive fractional differential equations involving Fredholm and Volterra integrals. This paper is mainly focused to the existence, uniqueness and stability of special random impulsive fractional differential equations with local initial conditions and nonlocal initial conditions se...

In this paper, we investigate the existence and Ulam–Hyers–Rassias stability results for a class of boundary value problems for implicit ψ-Caputo fractional differential equations with non-instantaneous impulses involving both retarded and advanced arguments. The results are based on the Banach contraction principle and Krasnoselskii’s fixed point...

The natural streamflow of the River is encouraged to forecast through multiple methods. The impartiality of this study is the comparison of the forecast accuracy rates of the time-series (TS) hybrid model with the conventional model. The behavior of the natural monthly statistical chaotic streamflow to use in the forecasting models has been compile...

In this paper, we establish the existence and stability results for the (ρk,φk)-Hilfer fractional integro-differential equations under instantaneous impulse with non-local multi-point fractional integral boundary conditions. We achieve the formulation of the solution to the (ρk , φk )-Hilfer fractional differential equation with constant coefficien...

In this article, we study the existence and uniqueness of multiple positive periodic solutions for a Gilpin--Ayala predator-prey model under consideration by applying asymptotically periodic functions. The result of this paper is completely new. By using Comparison Theorem and some technical analysis, we showed that the classical nonlinear fraction...

In this paper, we study the existence of solutions and their uniqueness and different kinds of Ulam-Hyers stability for a new class of nonlinear Caputo quantum boundary value problems. Also, we investigate such properties for the relevant generalized coupled q-system involving fractional quantum operators. By using the Banach contraction principle...

The objective of this manuscript is to establish a link between the concept of inequalities and Center-Radius order functions, which are intriguing due to their properties and widespread use. We introduce the notion of the CR (Center-Radius)-order interval-valued preinvex function with the help of a total order relation between two intervals. Furth...

In this paper, we apply the fractal-fractional derivative in the Atangana-Baleanu sense to a model of the human immunodeficiency virus infection of CD$ 4^{+} $ T-cells in the presence of a reverse transcriptase inhibitor, which occurs before the infected cell begins producing the virus. The existence and uniqueness results obtained by applying Bana...

This work solves the problem of thin-film withdrawal and drainage of a steady incompressible couple stress fluid on the outer surface of a vertical cylinder. The governing equations for velocity and temperature distributions are subjected to the boundary conditions and solved with the help of homotopy analysis method. The obtained expressions for f...

Among the renewable energies, there is geothermal energy, conventional air conditioning has negative consequences on the environment, to have an economical and sustainable solution: the EAHE respond to this concern. In the current study, the study of the thermal performance of the earth-air heat exchanger (EAHE) has been completed. For the impact o...

Results reported in this paper establish the existence of solutions for a class of generalized fractional inclusions based on the Caputo–Hadamard jerk system. Under some inequalities between multi-functions and with the help of special contractions and admissible maps, we investigate the existence criteria. Fixed points and end points are key roles...

The structured singular values and skewed structured singular values are the well-known mathematical quantities and bridge the gap between linear algebra and system theory. It is well-known fact that an exact computation of these quantities is NP-hard. The NP-hard nature of structured singular values and skewed structured singular values allow us t...

In this article, we investigate the existence and uniqueness of solutions for a nonlinear coupled system of Liouville–Caputo type fractional integro-differential equations supplemented with non-local discrete and integral boundary conditions. The nonlinearity relies both on the unknown functions and their fractional derivatives and integrals in the...

In this paper, we present the existence, uniqueness, and asymptotic behavior of mild solution for neutral stochastic impulsive integrodifferential equations driven by fractional Brownian motion and Brownian motion with the Hurst index H>1/2 with the nonlocal condition. The results are obtained by using Banach fixed point principle in a Hilbert spac...

A mathematical model of the nutrient-phytoplankton-zooplankton associated with viral infection in phytoplankton under the Atangana-Baleanu derivative in the Caputo sense is investigated in this study. We prove the theoretical results for the existence and uniqueness of the solutions by using Banach’s and Sadovskii’s fixed point theorems. The notion...

In this research, we suggest some convergence results for operators having (RCSC) condition in Banach space setting under F iterative scheme. We establish weak convergence under Opials condition and also establish some important strong convergence results under some appropriate assumptions on the domain or on the mapping. We furnish a non-trivial e...

In this manuscript, we analyze the existence, uniqueness and Ulam's stability for Caputo proportional fractional integro-differential equation involving mixed nonlocal conditions with respect to another function. The uniqueness result is proved via Banach's fixed point theorem and the existence results are established by using the Leray-Schauder no...

Building aeration ventilation may contribute to achieve thermal comfort there by economizing huge amount of electricity that would be supplied using conventional air conditioning systems. Natural ventilation maintains thermal equilibrium between heating and cooling balances. They may also be used in conjunction with other systems in certain circums...

The current work investigates the efficiency of a Direct Methanol Fuel Cell (DMFC) by using COMSOL. The set-up model takes into consideration the electrochemical kinetics and chemical reactions. The anode catalyst layers are a main element in the PEM fuel cell; their porosity significantly affects the fuel cell efficiency. We focus on the impact of...

A design of an optimal backstepping fractional order proportional integral derivative (FOPID) controller for handling the trajectory tracking problem of wheeled mobile robots (WMR) is examined in this study. Tuning parameters is a challenging task, to overcome this issue a hybrid meta-heuristic optimization algorithm has been utilized. This evoluti...

his study investigates a variety of novel estimations involving the expectation, variance, and moment functions of continuous random variables by applying a generalized proportional fractional integral operator. Additionally, a continuous random variable with a probability density function is presented in the context of the proportional Riemann–Lio...

This paper establishes a mathematical model of the Zika virus infection with the sexual transmission route under the generalized Caputo-type fractional derivative. The model consists of a system of eleven nonlinear fractional differential equations. The existence and uniqueness results are derived by applying Banach’s and Schaüder’s fixed point the...

In this manuscript, we study the existence and Ulam's stability results for impulsive multi-order Caputo proportional fractional pantograph differential equations equipped with boundary and integral conditions with respect to another function. The uniqueness result is proved via Banach's fixed point theorem, and the existence results are based on S...

This paper investigates existence, uniqueness, and Ulam’s stability results for a nonlinear implicit \phi-Hilfer FBVP describing Navier model with NIBCs. By Banach’s fixed point theorem, the unique property is established. Meanwhile, existence results are proved by using the fixed point theory of Leray-Schauder’s and Krasnoselskii’s types. In addit...

Thismanuscriptinvestigatesanextendedboundaryvalueproblemforafractionalpanto- graph differential equation with instantaneous impulses under the Caputo proportional fractional derivative with respect to another function. The solution of the proposed problem is obtained using Mittag–Leffler functions. The existence and uniqueness results of the propos...

In this paper, we establish sufficient conditions to approve the existence and uniqueness of solutions of a nonlinear implicit ψ-Hilfer fractional boundary value problem of the cantilever beam model with nonlinear boundary conditions. By using Banach’s fixed point theorem, the uniqueness result is proved. Meanwhile, the existence result is obtained...

Our main purpose in this paper is to prove the existence of solutions for the fractionalstrongly singular thermostat model under some generalized boundary conditions. In this way, weuse some recent nonlinear fixed-point techniques involvingα-ψ-contractions andα-admissible maps.Further, we establish the similar results for the hybrid version of the...

A mathematical model for the dynamic systems of $\mathbb{SMA}$ SMA involving the $\mathbb{ABC}$ ABC -fractional derivative is considered in this manuscript. We examine the basic reproduction number and analyze the stability of the equilibrium points. We prove the theoretical results of the existence and Ulam’s stability of the solutions for the pro...

In this paper, the existence and uniqueness of solutions for a nonlinear generalized proportional fractional functional integro-differential Langevin equation involving variable coefficient via nonlocal multi-point integral conditions are investigated by using Banach’s, Schaefer’s and Krasnoselskii’s fixed point theorems. Different types of Ulam–Hy...

In the present work a coupled system consisting by ψ-Hilfer fractional order Langevin equations supplemented with nonlocal integral boundary conditions is studied. Existence and uniqueness results are obtained by using standard fixed point theorems. The obtained results are well illustrated by numerical examples.

In this paper, a mathematical model of generalized fractional-order is constructed to study the problem of human immunodeficiency virus (HIV) infection of CD$4^+$ T-cells with treatment. The model consists of a system of four nonlinear differential equations under the generalized Caputo fractional derivative sense. The existence results for the fra...

In this paper, we discuss existence and stability results for a new class of impulsive fractional boundary value problems with non-separated boundary conditions containing the Caputo proportional fractional derivative of a function with respect to another function. The uniqueness result is discussed via Banach's contraction mapping principle, and t...

In this research study, we are concerned with the existence and stability of solutions of a boundary value problem (BVP) of the fractional thermostat control model with ψ -Hilfer fractional operator. We verify the uniqueness criterion via the Banach fixed-point principle and establish the existence by using the Schaefer and Krasnoselskii fixed-poin...

In this paper, we investigate existence, uniqueness and four different types of Ulam's stability, that is, Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability and generalized Ulam-Hyers-Rassias stability of the solution for a class of nonlinear fractional Pantograph differential equation in term of a proportional Ca...

In this paper, we provide new generalizations for the Gronwall’s inequality in terms of a ψ-fractional operator. The new forms of Gronwall’s inequality are obtained within a general platform that includes several existing results as particular cases. To apply our results and examine their validity, we prove the existence and uniqueness of solutions...

We deal with semilinear functional special random impulsive differential equations in this paper. Contraction mapping principle is used to study the existence and uniqueness of the mild solution of the system. Again we have established ulam stabilities, exponential stability and stability of the system, where the sufficient conditions for stability...

In this paper, we discuss the existence, uniqueness and stability of boundary value problems for $\psi$-Hilfer fractional integro-differential equations with mixed nonlocal (multi-point, fractional derivative multi-order and fractional integral multi-order) boundary conditions. The uniqueness result is proved via Banach's contraction mapping pr...

In this paper, we investigate the existence and uniqueness of a solution for a class of ψ -Hilfer implicit fractional integro-differential equations with mixed nonlocal conditions. The arguments are based on Banach’s, Schaefer’s, and Krasnosellskii’s fixed point theorems. Further, applying the techniques of nonlinear functional analysis, we establi...

Results reported in this paper study the existence and stability of a class of implicit generalized proportional fractional integro-differential Langevin equations with nonlocal fractional integral conditions. The main theorems are proved with the help of Banach’s, Krasnoselskii’s, and Schaefer’s fixed point theorems and Ulam’s approach. Finally, a...

In this paper, we study the oscillatory behavior of solutions for a type of generalized proportional fractional differential equations with forcing and damping terms. Several oscillation criteria are established for the proposed equations in terms of Riemann-Liouville and Caputo settings. The results of this paper generalize some existing theorems...

In this paper, we study the Langevin equation within the generalized proportional fractional derivative. The proposed equation involves a variable coefficient and subjects to mixed integro-differential boundary conditions. We introduce the generalized proportional fractional derivative and expose some of its features. We mainly investigate the exis...

In this paper, sufficient conditions are established for the oscillation of all solutions of generalized proportional fractional differential equations of the form        a D α,ρ x(t) + ξ 1 (t, x(t)) = µ(t) + ξ 2 (t, x(t)), t > a ≥ 0, lim t→a + a I j−α,ρ x(t) = b j , j = 1, 2,. .. , n, where n = α, a D α,ρ is the generalized proportional fra...

New versions of a Gronwall–Bellman inequality in the frame of the generalized (Riemann–Liouville and Caputo) proportional fractional derivative are provided. Before proceeding to the main results, we define the generalized Riemann–Liouville and Caputo proportional fractional derivatives and integrals and expose some of their features. We prove our...

In this paper, we provide a new version for the Gronwall inequality in the frame of the generalized proportional fractional derivative. Prior to the main results, we introduce the generalized proportional fractional derivative and expose some of its features. As an application, we accommodate the newly defined derivative to prove the uniqueness and...

In this paper, we introduce new concepts of Hahn difference operator, the qk,ωk\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$q_{k},\omega_{k}$\end{document}-Hahn diffe...

We obtain some existence and uniqueness results for an impulsively hybrid fractional quantum Langevin (qk-difference) equation involving a new qk-shifting operator and supplemented with non-separated boundary conditions containing Caputo qk-fractional derivatives. Our first result, relying on Banach’s fixed point theorem, is concerned with the exis...

In this paper, we discuss the existence of solutions for a first order boundary value problem for impulsive functional qk-integro-difference inclusions. Some new existence results are obtained for convex as well as non-convex multivalued maps with the aid of some classical fixed point theorems. Illustrative examples are also presented.

In this paper we study existence and uniqueness of solutions for coupled systems consisting from fractional differential equations of Riemann-Liouville type subject to coupled and uncoupled Hadamard fractional integral boundary conditions. The existence and uniqueness of solutions is established by Banach’s contraction principle, while the existenc...

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.

In this paper, some new mixed type Riemann-Liouville and Hadamard fractional integral inequalities are established, in the case where the functions are bounded by integrable functions. Moreover, mixed type Riemann-Liouville and Hadamard fractional integral inequalities of Chebyshev type are presented.

In this paper we prove several fractional quantum integral inequalities for the new q-shifting operator Φqa(m)=qm+(1−q)a\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${...

Fractional differential equations have been shown to be very useful in the study of models of many phenomena in various fields of science and engineering, such as physics, chemistry, biology, signal and image processing, biophysics, blood flow phenomena, control theory, economics, aerodynamics, and fitting of experimental data. Much of the work on...

In this paper we establish some new quantum integral inequalities for convex functions.

In this paper, we study a new class of boundary value problems from a fractional differential inclusion of Riemann-Liouville type and nonlocal Hadamard fractional integral boundary conditions. Some new existence results for convex as well as non-convex multi-valued maps are obtained using standard fixed point theorems. The obtained results are illu...

Recently the authors introduced in [1] the notions of q k-derivative and q k-integral of a function on finite intervals. As application's existence and uniqueness results for initial value problems for first and second-order impulsive q k-difference equations were proved. In this paper, we study the existence and uniqueness of solutions for a bound...

In this paper, we introduce a new class of boundary value problems consisting of a fractional differential equation of Riemann-Liouville type, D q R L x ( t ) = f ( t , x ( t ) ) , t ∈ [ 0 , T ] , subject to the Hadamard fractional integral conditions x ( 0 ) = 0 , x ( T ) = ∑ i = 1 n α i H I p i x ( η i ) . Existence and uni...

In this paper, we study the existence and uniqueness of solutions for fractional boundary value problems involving nonlocal fractional integral boundary conditions, by means of standard fixed point theorems. Some illustrative examples are also presented. MSC: 26A33, 34A08, 34B15.

We establish new fractional integral inequalities, via Hadamard's fractional integral. Several new integral inequalities are obtained, including a Grüss type Hadamard fractional integral inequality, by using Young and weighted AM-GM inequalities. Many special cases are also discussed.

In this paper, some new fractional integral inequalities are established.

We are concerned with the existence of at least one, two or three positive solutions for the boundary value problem with three-point multi-term fractional integral boundary conditions: { D(q)u(t) + f(t,u(t) = 0, 1 < q <= 2, 0 < t <1, u(0) = 0, u(1) = Sigma(m)(i=1) alpha(I-pi u)(eta) 0 < eta < 1, where D-q is the standard Riemann-Liouville fractiona...

In this article, we study a nonlinear fractional integro-differential Langevin equation involving two fractional orders with three-point multi-term fractional integral boundary conditions. By using fixed point theorems and Leray-Schauder degree theory, some new existence results are obtained. Two examples illustrate our results.

In this paper is concerned with the existence of solutions for nonlinear second-order q-difference equations with three-point multi-term q- integral boundary conditions. Some new existence results are obtained by using Banach's contraction mapping, Krasnoselskii's fixed point theorem and Leray-Schauder degree theory. As an application, we give two...

In this article, we present some new existence and uniqueness results for nonlinear fractional integro-differential equations with m-point multi-term fractional order integral boundary conditions. Our results are based on the Banach contraction principle and Krasnoselskii’s fixed point theorem. MSC: 26A33, 34B15.

By using standard fixed point theorems and Leray-Schauder degree theory, we study the existence of solutions for nonlinear fractional differential equations with m-point boundary condition c D q u=f(t,u(tt)),0<t<1,u(0)=0,u(1)=∑ i=1 m-1 α i ∫ η i-1 η i u(s)ds, where 1<q≤2,0=η 0 <η 1 <η 2 <⋯<η m-2 <η m-1 =1,∑ i=1 m-1 α i (η i 2 -η i-1 2 )≠2 are given...

This article studies a boundary value problem of nonlinear fractional differential equations with three-point fractional integral boundary conditions. Some new existence results are obtained by applying standard fixed point theorems. As an application, we give two examples that illustrate our results. MSC: 26A33, 34B15.

We study sufficient conditions for the existence of positive solutions to the m-point integral boundary value problem u'' + a(t)f(u) = 0, t ∈ (0, 1), αi ≥ 0 for i ∈ {1,..., m - 3} ∪ {m - 1} and α m-2 > 0. α ∈ C ([0,1], [0,∞)) and f ∈ C ([0,∞), [0,∞)). We show the existence of at least one positive solution if f is either superlinear or sublinear by...