Abstract
In this paper, we study a coupled system of Caputo-Hadamard type sequential fractional differential equations supplemented with nonlocal boundary conditions involving Hadamard fractional integrals. The sufficient criteria ensuring the existence and uniqueness of solutions for the given problem are obtained. We make use of the Leray-Schauder alternative and contraction mapping principle to derive the desired results. Illustrative examples for the main results are also presented.
Highlights
Fractional calculus has emerged as an important area of investigation in view of its extensive applications in mathematical modeling of many complex and nonlocal nonlinear systems
We introduce a new class of boundary value problems consisting of Caputo-Hadamard type fractional differential equations and Hadamard type fractional integral boundary conditions
We have developed the existence theory for a nonlocal integral boundary value problem of coupled sequential fractional differential equations involving Caputo-Hadamard fractional derivatives and Hadamard fractional integrals
Summary
Fractional calculus has emerged as an important area of investigation in view of its extensive applications in mathematical modeling of many complex and nonlocal nonlinear systems. Fractional differential equations involving Hadamard derivative attracted significant attention in recent years, for instance, see [10,11,12,13,14,15,16,17,18,19,20] and the references cited therein. One can find some recent results on Caputo-Hadamard type fractional differential equations in [22,23,24,25,26,27,28] and the references cited therein. We introduce a new class of boundary value problems consisting of Caputo-Hadamard type fractional differential equations and Hadamard type fractional integral boundary conditions.
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