Abstract
In this paper, we examine the consequences of existence, uniqueness and stability of a multi-point boundary value problem defined by a system of coupled fractional differential equations involving Hadamard derivatives. To prove the existence and uniqueness, we use the techniques of fixed point theory. Stability of Hyers-Ulam type is also discussed. Furthermore, we investigate variations of the problem in the context of different boundary conditions. The current results are verified by illustrative examples.
Highlights
Due to its broad applications in mathematical modeling of many complex and non-local nonlinear systems, fractional calculus has emerged as an important field of investigation
The Hadamard fractional derivative contains a logarithmic function of an arbitrary exponent in the integral kernel, which appears in its description
We extend the boundary value problem of Wang et al [36] to nonlinear coupled system of Hadamard fractional differential equations having the Hadamard derivative value of the unknown function at T is propositional to the sum of Hadamard integral values of the unknown function on the strips (1, υ), (1, θ ) and multi-points values of the unknown functions with different strip lengths (1, υ), (1, θ ) and with different multipoint δj, γj, j = 1, 2, . . . , k – 2
Summary
Uniqueness and stability analysis of a coupled fractional-order differential systems involving Hadamard derivatives and associated with multi-point boundary conditions.
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