RIEMANN–LIOUVILLE FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS WITH FRACTIONAL NONLOCAL MULTI-POINT BOUNDARY CONDITIONS

Bashir Ahmad, Badrah Alghamdi (), Ravi P. Agarwal and Ahmed Alsaedi ()
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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
Badrah Alghamdi: 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
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

FRACTALS (fractals), 2022, vol. 30, issue 01, 1-11

Abstract: In this paper, we investigate the existence and uniqueness of solutions for Riemann–Liouville fractional integro-differential equations equipped with fractional nonlocal multi-point and strip boundary conditions in the weighted space. The methods of our study include the well-known tools of the fixed point theory, which are commonly applied to establish the existence theory for the initial and boundary value problems after converting them into the fixed point problems. We also discuss the case when the nonlinearity depends on the Riemann–Liouville fractional integrals of the unknown function. Numerical examples illustrating the main results are presented.

Keywords: Riemann–Liouville Fractional Derivative; Integro-Differential Equations; Nonlocal Multi-Point Boundary Conditions; Existence; Fixed Point (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22400023

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