On a boundary value problem for fractional Hahn integro-difference equations with four-point fractional integral boundary conditions

<abstract><p>In this paper, we study a boundary value problem consisting of Hahn integro-difference equation supplemented with four-point fractional Hahn integral boundary conditions. The novelty of this problem lies in the fact that it contains two fractional Hahn difference operators and three fractional Hahn integrals with different quantum numbers and orders. Firstly, we convert the given nonlinear problem into a fixed point problem, by considering a linear variant of the problem at hand. Once the fixed point operator is available, we make use the classical Banach's and Schauder's fixed point theorems to establish existence and uniqueness results. An example is also constructed to illustrate the main results. Several properties of fractional Hahn integral that will be used in our study are also discussed.</p></abstract>

On Sequential Fractional q-Hahn Integrodifference Equations

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 Hahn calculus simultaneously.

Existence Results of a Coupled System of Caputo Fractional Hahn Difference Equations with Nonlocal Fractional Hahn Integral Boundary Value Conditions

In this article, we propose a coupled system of Caputo fractional Hahn difference equations with nonlocal fractional Hahn integral boundary conditions. The existence and uniqueness result of solution for the problem is studied by using the Banach’s fixed point theorem. Furthermore, the existence of at least one solution is presented by using the Schauder fixed point theorem.

Existence Results for Fractional Hahn Difference and Fractional Hahn Integral Boundary Value Problems

The existence and uniqueness results of two fractional Hahn difference boundary value problems are studied. The first problem is a Riemann-Liouville fractional Hahn difference boundary value problem for fractional Hahn integrodifference equations. The second is a fractional Hahn integral boundary value problem for Caputo fractional Hahn difference equations. The Banach fixed-point theorem and the Schauder fixed-point theorem are used as tools to prove the existence and uniqueness of solution of the problems.