EXISTENCE RESULTS FOR A COUPLED SYSTEM OF NONLINEAR FRACTIONAL q-INTEGRO-DIFFERENCE EQUATIONS WITH q-INTEGRAL-COUPLED BOUNDARY CONDITIONS

Ahmed Alsaedi (), Hana Al-Hutami (), Bashir Ahmad and Ravi P. Agarwal
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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
Ravi P. Agarwal: 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†Department of Mathematics, Texas A & M University, Kingsville, Texas 78363-8202, USA

FRACTALS (fractals), 2022, vol. 30, issue 01, 1-19

Abstract: In this paper, we introduce and investigate a new class of coupled fractional q-integro-difference equations involving Riemann–Liouville fractional q-derivatives and q-integrals of different orders, equipped with q-integral-coupled boundary conditions. The given problem is converted into an equivalent fixed-point problem by introducing an operator whose fixed-points coincide with solutions of the problem at hand. The existence and uniqueness results for the given problem are, respectively, derived by applying Leray–Schauder nonlinear alternative and Banach contraction mapping principle. Illustrative examples for the obtained results are constructed. This paper concludes with some interesting observations and special cases dealing with uncoupled boundary conditions, and non-integral and integral types nonlinearities.

Keywords: Riemann–Liouville Fractional q-Derivative; Fractional q-Integral; System; Boundary Conditions; Existence; Fixed Point (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22400424

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