On a boundary value problem for fractional hahn integro-difference equations with four-point fractional integral boundary conditions
Date
2022
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American Institute of Mathematical Sciences
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On a boundary value problem for fractional hahn integro-difference equations with four-point fractional integral boundary conditions
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Abstract
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 BanachÕs and SchauderÕs 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. © 2022 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0).
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AIMS Mathematics