Sequential Riemann–Liouville and Hadamard–Caputo Fractional Differential Systems with Nonlocal Coupled Fractional Integral Boundary Conditions
Chanakarn Kiataramkul, Weera Yukunthorn, Sotiris K. Ntouyas, Jessada Tariboon
Abstract
In this paper, we initiate the study of existence of solutions for a fractional differential system which contains mixed Riemann–Liouville and Hadamard–Caputo fractional derivatives, complemented with nonlocal coupled fractional integral boundary conditions. We derive necessary conditions for the existence and uniqueness of solutions of the considered system, by using standard fixed point theorems, such as Banach contraction mapping principle and Leray–Schauder alternative. Numerical examples illustrating the obtained results are also presented.
Topics & Concepts
MathematicsHadamard transformUniquenessFractional calculusContraction principleMathematical analysisBoundary value problemFixed-point theoremContraction mappingPure mathematicsApplied mathematicsFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisDifferential Equations and Numerical Methods