Hilfer–Hadamard Fractional Boundary Value Problems with Nonlocal Mixed Boundary Conditions

Fractal and Fractional

Sotiris K. Ntouyas¹  Bashir Ahmad² 

[1] Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece;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;

关键词: Hilfer–Hadamard fractional derivative;    Riemann–Liouville fractional derivative;    Caputo fractional derivative;    fractional differential equations;    inclusions;    nonlocal boundary conditions;   

DOI  :  10.3390/fractalfract5040195

来源: DOAJ

【 摘 要 】

This paper is concerned with the existence and uniqueness of solutions for a Hilfer–Hadamard fractional differential equation, supplemented with mixed nonlocal (multi-point, fractional integral multi-order and fractional derivative multi-order) boundary conditions. The existence of a unique solution is obtained via Banach contraction mapping principle, while the existence results are established by applying the fixed point theorems due to Krasnoselskiĭ and Schaefer and Leray–Schauder nonlinear alternatives. We demonstrate the application of the main results by presenting numerical examples. We also derive the existence results for the cases of convex and non-convex multifunctions involved in the multi-valued analogue of the problem at hand.

【 授权许可】

Unknown