Abstract
In this paper, the existence and uniqueness of the solutions to a fractional order nonlinear coupled system with integral boundary conditions is investigated. Furthermore, Ulam’s type stability of the proposed coupled system is studied. Banach’s fixed point theorem is used to obtain the existence and uniqueness of the solutions. Finally, an example is provided to illustrate the analytical findings.
Highlights
Fractional calculus is a branch of mathematical analysis, in which arbitrary order differential and integral operators are studied
Existence and uniqueness of solutions for fractional order differential systems in finite dimensional as well infinite dimensional spaces were studied by several authors [7,8,9,10,11]
One can generalize the same concept of stability to a neutral time delay system/inclusion as well as state delay system/inclusion, which have some useful scientific applications
Summary
Fractional calculus is a branch of mathematical analysis, in which arbitrary order differential and integral operators are studied. To the best of our knowledge, there are only few manuscripts devoted to the study of Ulam’s type stability for coupled system of fractional differential equations. There is no manuscript considering the Ulam’s stability for coupled system of fractional order α ∈ Motivated by this fact, in this paper, the existence, uniqueness of solutions as well as Ulam’s type stability for the considered coupled system involving Caputo derivative is studied. A few examples are given to show the application of the obtained abstract results
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