Abstract
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.
Highlights
Jackson [ ] initiated quantum calculus or q-difference calculus that can describe many phenomena in various fields of science and engineering
A class of integral boundary value problems appeared in different areas of applied mathematics and physics
For comments on the importance of integral boundary problems, we refer the reader to the papers by Webb and Infante [, ], Gallardo [ ], Karakostas and Tsamatos [ ], Lomtatidze and Malaguti [ ], and the references therein
Summary
Jackson [ ] initiated quantum calculus or q-difference calculus that can describe many phenomena in various fields of science and engineering. Almeida and Martins [ ] proposed the following fractional q-difference equation with three-point integral boundary conditions: There is a development of boundary value problems for fractional q-difference equations showing an operation of the investigative function.
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