Nonlocal Fractional Boundary Value Research Articles

Nonlocal and multiple-point fractional boundary value problem in the frame of a generalized Hilfer derivative

The aim of this manuscript is to handle the nonlocal boundary value problem for a specific kind of nonlinear fractional differential equations involving a ξ-Hilfer derivative. The used fractional operator is generated by the kernel of the kind k(vartheta,s)=xi (vartheta )-xi (s) and the operator of differentiation { D}_{xi } = ( frac{1}{xi ^{prime }(vartheta )}frac{d}{dvartheta } ) . The existence and uniqueness of solutions are established for the considered system. Our perspective relies on the properties of the generalized Hilfer derivative and the implementation of Krasnoselskii’s fixed point approach and Banach’s contraction principle with respect to the Bielecki norm to obtain the uniqueness of solution on a bounded domain in a Banach space. Besides, we discuss the Ulam–Hyers stability criteria for the main fractional system. Finally, some examples are given to illustrate the viability of the main theories.

On a coupled system of fractional sum-difference equations with p-Laplacian operator

In this paper, we propose a nonlocal fractional sum-difference boundary value problem for a coupled system of fractional sum-difference equations with p-Laplacian operator. The problem contains both Riemann–Liouville and Caputo fractional difference with five fractional differences and four fractional sums. The existence and uniqueness result of the problem is studied by using the Banach fixed point theorem.

Existence Results for Nonlocal Multi-Point and Multi-Term Fractional Order Boundary Value Problems

In this paper, we discuss the existence and uniqueness of solutions for a new class of multi-point and integral boundary value problems of multi-term fractional differential equations by using standard fixed point theorems. We also demonstrate the application of the obtained results with the aid of examples.

On the Nonlocal Fractional Delta-Nabla Sum Boundary Value Problem for Sequential Fractional Delta-Nabla Sum-Difference Equations

In this paper, we propose sequential fractional delta-nabla sum-difference equations with nonlocal fractional delta-nabla sum boundary conditions. The Banach contraction principle and the Schauder’s fixed point theorem are used to prove the existence and uniqueness results of the problem. The different orders in one fractional delta differences, one fractional nabla differences, two fractional delta sum, and two fractional nabla sum are considered. Finally, we present an illustrative example.

On nonlocal fractional symmetric Hanh integral boundary value problems for fractional symmetric Hahn integrodifference equation

In this paper, we propose a boundary value problems for fractional symmetric Hahn integrodifference equation. The problem contains two fractional symmetric Hahn difference operators and three fractional symmetric Hahn integral with different numbers of order. The existence and uniqueness result of problem is studied by using the Banach fixed point theorem. The existence of at least one solution is also studied, by using Schauder's fixed point theorem.

On nonlocal fractional sum-difference boundary value problems for Caputo fractional functional difference equations with delay

In this article, we study the existence and uniqueness results for a nonlocal fractional sum-difference boundary value problem for a Caputo fractional functional difference equation with delay, by using the Schauder fixed point theorem and the Banach contraction principle. Finally, we present some examples to display the importance of these results.

On nonlocal fractional q-integral boundary value problems of fractional q-difference and fractional q-integrodifference equations involving different numbers of order and q

In this paper, we study some new class of nonlocal three-point fractional q-integral boundary value problems of a nonlinear fractional q-difference equation and a nonlinear fractional q-integrodifference equation. Our problems contain different numbers of order and q in derivatives and integrals. The existence and uniqueness results are based on Banach’s contraction mapping principle and Krasnoselskii’s fixed point theorem. In addition, some examples are presented to illustrate the importance of these results.