Abstract
Fractional-order boundary value problems are used to model certain phenomena in chemistry, physics, biology, and engineering. However, some of these models do not meet the existence and uniqueness required in the mainstream of mathematical processes. Therefore, in this paper, the existence, stability, and uniqueness for the solution of the coupled system of the Caputo-type sequential fractional differential equation, involving integral boundary conditions, was discussed, and investigated. Leray–Schauder’s alternative was applied to derive the existence of the solution, while Banach’s contraction principle was used to examine the uniqueness of the solution. Moreover, Ulam–Hyers stability of the presented system was investigated. It was found that the theoretical-related aspects (existence, uniqueness, and stability) that were examined for the governing system were satisfactory. Finally, an example was given to illustrate and examine certain related aspects.
Highlights
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The fractional calculus essentially involves differentiation and integration to an arbitrary order, which is considered as an important tools that have facilitated many real-life phenomena in considerable fields such as physics, biology, and chemistry
Motivated by the above discussion and our review of the literature, this paper aims to discuss and analyze the following coupled system of Caputo-type sequential fractional differential equations
Summary
The field of fractional-order boundary value problems has been discussed by several scientific researchers across the world. This is evident from the number of significant studies of fractional-order boundary value problems that mainly focus on extending and transforming such problems from the theoretical to the application aspect, in order to make them applicable for certain real-life phenomena. The fractional calculus essentially involves differentiation and integration to an arbitrary order, which is considered as an important tools that have facilitated many real-life phenomena in considerable fields such as physics, biology, and chemistry (see [1,2,3,4]). Engineering is considered to be one of the main fields that benefits from fractional calculus, due to providing a full and comprehensive description of some complex engineering models
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