372 Results Found

In this work, we present a boundary value problem of hybrid functional differential inclusion with nonlocal condition. The boundary conditions of integral and infinite points will be deduced. The existence of solutions and its maximal and minimal wil...

We consider a two-step numerical approach for solving parabolic initial boundary value problems in 3D simply connected smooth regions. The method uses the Laplace transform in time, reducing the problem to a set of independent stationary boundary val...

This paper studies a class of integral boundary value problem of fractional q-difference equations. We first give an explicit expression for the associated Green’s function and obtain an important property of the function. The new property allo...

In this paper, under some super- and sub-linear growth conditions, we study the existence of positive solutions for a high-order Riemann–Liouville type fractional integral boundary value problem involving fractional derivatives. Our analysis me...

In this paper, the a priori estimate method, the so-called energy inequalities method based on some functional analysis tools is developed for a Caputo time fractional $2m$ th order diffusion wave equation with purely nonlocal conditions of int...

In this paper, we use the fixed-point index to establish positive solutions for a system of Riemann–Liouville type fractional-order integral boundary value problems. Some appropriate concave and convex functions are used to characterize couplin...

We study fixed-point theorems of contractive mappings in b-metric space, cone b-metric space, and the newly introduced extended b-metric space. To generalize an existence and uniqueness result for the so-called ${\mathsf{\Phi }}_s$ functions in the b-metric space...

The authors investigate the existence of solutions to a class of boundary value problems for fractional q-difference equations in a Banach space that involves a q-derivative of the Caputo type and nonlinear integral boundary conditions. Their result...

In the paper, we investigate a local boundary value problem with transmitting condition of the integral form for mixed parabolic-hyperbolic equation with non-characteristic line of type changing. Theorem on strong solvability of the considered proble...

In this paper, we prove the sufficient conditions for the existence results of a solution of a nonlocal q-symmetric integral boundary value problem for a sequential q-symmetric integrodifference equation by using the Banach’s contraction mappin...

The numerical solution to boundary differential problems is a crucial task in modern applied mathematics. Usually, implicit integration methods are applied to solve this class of problems due to their high numerical stability and convergence. The kno...

We discuss the existence criteria and Ulam–Hyers stability for solutions to a nonlocal integral boundary value problem of nonlinear coupled Hilfer–Hadamard-type fractional Langevin equations. Our results rely on the Leray–Schauder a...

In this paper, we investigate the existence of an absolute continuous solution to a class of first-order nonlinear differential equation with integral boundary conditions (BCs) or with infinite-point BCs. The Liouville-Caputo fractional derivative is...

In this paper, we were interested in obtaining the exact expression and studying the regions of constant sign of Green’s function related to a second-order perturbed periodic problem coupled with integral boundary conditions at the extremes of the in...

We study the existence results of a fractional (p, q)-integrodifference equation with periodic fractional (p, q)-integral boundary condition by using Banach and Schauder’s fixed point theorems. Some properties of (p, q)-integral are also presented in...

Symmetry can play an important role in the study of boundary value problems, which are a type of problem in mathematics that involves finding the solutions to differential equations subject to given boundary conditions. Integral transforms play a cru...

We begin by introducing some function spaces $L_c^p\left({\mathbb{R}}^{+}\right),X_c^p\left(J\right)$ made up of integrable functions with exponent or power weights defined on infinite intervals, and then we investigate the properties of Mellin convolution operators mapping on these spaces,...

In this work, we address the solvability of a Riemann–Liouville-type fractional-impulsive integral boundary value problem. Under some conditions on the spectral radius corresponding to the related linear operator, we use fixed-point methods to...

In this paper, we study a boundary value problem involving $(p,q)$-integrodifference equations, supplemented with nonlocal fractional $(p,q)$-integral boundary conditions with respect to asymmetric operators. First, we convert the given nonlinear problem...

In this paper, we introduce and thoroughly examine new generalized $\psi$-conformable fractional integral and derivative operators associated with the auxiliary function $\psi \left(t\right)$. We rigorously analyze and confirm the essential properties of...

In this survey paper, we start with a discussion of the general fractional derivative (GFD) introduced by A. Kochubei in his recent publications. In particular, a connection of this derivative to the corresponding fractional integral and the Sonine r...

This study utilizes approximation techniques to address a boundary value problem involving a differential equation with a delayed argument. The problem is approached through analytical techniques by transforming it firstly into an equivalent integral...

We propose here a general framework covering a wide range of fractional operators for vector-valued functions. We indicate to what extent the case in which assumptions are expressed in terms of weak topology is symmetric to the case of norm topology....

The aim of this article is to present a procedure for the factorization and exact solution of boundary value problems for a class of n-th order linear Fredholm integro-differential equations with multipoint and integral boundary conditions. We use th...

In this article, we present a nonlocal Neumann boundary value problems for separate sequential fractional symmetric Hahn integrodifference equation. The problem contains five fractional symmetric Hahn difference operators and one fractional symmetric...

In the present research, single and multi-valued (k,ψ)-Hilfer type fractional boundary value problems of order in (1,2] involving nonlocal integral boundary conditions were studied. In the single-valued case, the Banach and Krasnosel’ski...

We investigate the existence of positive solutions for a class of fractional differential equations of arbitrary order $\delta >2$, subject to boundary conditions that include an integral operator of the fractional type. The consideration of this type of...

The primary aim of this manuscript is to establish unique fixed point results for a class of $\Psi$-contraction operators in complete G-metric spaces. By combining and extending various fixed point theorems in the context of $\Psi$-contraction operator...

A scalar nonlinear impulsive differential equation with a delay and generalized proportional Caputo fractional derivatives (IDGFDE) is investigated. The linear boundary value problem (BVP) for the given fractional differential equation is set up. The...

In this paper, we study and investigate an interesting Caputo fractional derivative and Riemann–Liouville integral boundary value problem (BVP): ^c $D_{0^{+}}^{q}u\left(t\right)=f(t,u\left(t\right)),t\in [0,T]$ , ${\displaystyle u^{\left(k\right)}}$...

We solve the boundary value problem for Einstein’s gravitational field equations in the presence of matter in the form of an incompressible perfect fluid of density $\rho$ and pressure field $p\left(r\right)$ located in a ball $r\le r_0$. We find a 1-parameter...

This paper investigates existence, uniqueness, and Ulam’s stability results for a nonlinear implicit $\psi$-Hilfer $\mathbb{FBVP}$ describing Navier model with $\mathbb{NIBC}$s. By Banach’s fixed point theorem, the unique property is established. Meanwhile, exi...

In this paper, we establish the existence and stability results for the $({\rho }_k,{\varphi }_k)$-Hilfer fractional integro-differential equations under instantaneous impulse with non-local multi-point fractional integral boundary conditions. We achieve the f...

In this paper, we study boundary value problems for differential inclusions, involving Hilfer fractional derivatives and nonlocal integral boundary conditions. New existence results are obtained by using standard fixed point theorems for multivalued...

In this paper, we consider the existence of multiple positive solutions to boundary value problems of nonlinear fractional differential equation with integral boundary conditions and parameter dependence. To obtain our results, we used a functional-t...

In the present article, we study a new class of sequential boundary value problems of fractional order differential equations and inclusions involving $\psi$-Hilfer fractional derivatives, supplemented with integral multi-point boundary conditions. The ma...

The initial boundary-value problem associated to a semilinear wave equation with time-dependent boundary values was approximated by using the method of lines. Time integration is achieved by means of an explicit time method obtained from an arbitrari...

In this paper, we study the existence of solutions for nonlocal single and multi-valued boundary value problems involving right-Caputo and left-Riemann–Liouville fractional derivatives of different orders and right-left Riemann–Liouville...

In recent years, the numerical solution of differential problems, possessing constants of motion, has been attacked by imposing the vanishing of a corresponding line integral. The resulting methods have been, therefore, collectively named (discrete)...

The numerical solution of fractional-order elliptic problems is investigated in bounded domains. According to real-life situations, we assumed inhomogeneous boundary terms, while the underlying equations contain the full-space fractional Laplacian op...

This study is intended to evaluate numerically the solution of second order boundary value problems (BVPs) subject to mixed boundary conditions using a direct method. The mixed set of boundary conditions is subsumed under Type 1: mixed boundary condi...

In this paper, we consider the existence of positive solutions for a singular tempered fractional equation with a p-Laplacian operator. By constructing a pair of suitable upper and lower solutions of the problem, some new results on the existence of...

The main goal of this paper is to present a new numerical algorithm for solving two models of one-dimensional fractional partial differential equations (FPDEs) subject to initial conditions (ICs) and integral boundary conditions (IBCs). This paper bu...

The concept of a $\beta$-integrated resolving function for a linear equation with a Gerasimov–Caputo fractional derivative is introduced into consideration. A number of properties of such functions are proved, and conditions for the solvability...

We study the existence of solutions for a new class of boundary value problems of arbitrary order fractional differential equations and inclusions, supplemented with integro-multistrip-multipoint boundary conditions. Suitable fixed point theorems are...

In the present article we study existence and uniqueness results for a new class of boundary value problems consisting by non-instantaneous impulses and Caputo fractional derivative of a function with respect to another function, supplemented with Ri...

In this paper, we discuss the existence and uniqueness of solutions for a new class of single and multi-valued boundary value problems involving both Riemann–Liouville and Caputo fractional derivatives, and nonlocal fractional integro-different...

In this paper, we prove existence and uniqueness results for a fractional sequential fractional q-Hahn integrodifference equation with nonlocal mixed fractional q and fractional Hahn integral boundary condition, which is a new idea that studies q and...

The work is dedicated to mathematical modelling of random diffusion flows of admixture particles in a two-phase stratified strip with stochastic disposition of phases and random thickness of inclusion-layers. The study of such models are especially i...

In this paper, we report on recent findings in the numerical solution of Hamiltonian Partial Differential Equations (PDEs) by using energy-conserving line integral methods in the Hamiltonian Boundary Value Methods (HBVMs) class. In particular, we con...