INVESTIGATION OF A NONLINEAR MULTI-TERM IMPULSIVE ANTI-PERIODIC BOUNDARY VALUE PROBLEM OF FRACTIONAL q-INTEGRO-DIFFERENCE EQUATIONS

Ahmed Alsaedi (), Hana Al-Hutami () and Bashir Ahmad
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Ahmed Alsaedi: Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia
Hana Al-Hutami: Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia
Bashir Ahmad: Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia

FRACTALS (fractals), 2023, vol. 31, issue 10, 1-18

Abstract: In this paper, we introduce and investigate a new class of nonlinear multi-term impulsive anti-periodic boundary value problems involving Caputo type fractional q-derivative operators of different orders and the Riemann–Liouville fractional q-integral operator. The uniqueness of solutions to the given problem is proved with the aid of Banach’s fixed point theorem. Applying a Shaefer-like fixed point theorem, we also obtain an existence result for the problem at hand. Examples are constructed for illustrating the obtained results. The paper concludes with certain interesting observations concerning the reduction of the results proven in the paper to some new results under an appropriate choice of the parameters involved in the governing equation.

Keywords: Fractional q-Derivative Operator; Riemann–Liouville Fractional q-Integral Operator; Impulse; Anti-Periodic Boundary Conditions; Existence of a Solution (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23401916

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