Abstract
This paper is devoted to generalizing the standard system of Navier boundary value problems to a fractional system of coupled sequential Navier boundary value problems by using terms of the Caputo derivatives. In other words, for the first time, we design a multi-term fractional coupled system of Navier equations under the fractional boundary conditions. The existence theory is studied regarding solutions of the given coupled sequential Navier boundary problems via the Krasnoselskii’s fixed-point theorem on two nonlinear operators. Moreover, the Banach contraction principle is applied to investigate the uniqueness of solution. We then focus on the Hyers–Ulam-type stability of its solution. Furthermore, the approximate solutions of the proposed coupled fractional sequential Navier system are obtained via the generalized differential transform method. Lastly, the results of this research are supported by giving simulated examples.
Highlights
Accepted: 5 October 2021Fractional differential equations (FDEs) are considered an important area of research in the direction of the applications of fractional calculus
We investigate some sufficient conditions to obtain H-U-stability results of the solutions to the coupled sequential FBVPs of Navier model (1)
By means of a fixed point theorem due to Krasnoselskii, we studied the existence criterion for solutions of a system of coupled sequential Navier FBVPs and investigated its uniqueness by terms of the contraction principle due to Banach
Summary
Accepted: 5 October 2021Fractional differential equations (FDEs) are considered an important area of research in the direction of the applications of fractional calculus. In the last few years, a large number of studies regarding the existence theory for different FDEs have received much attentions from researchers and some examples include [3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18]. Since we can model some of applied phenomena in the framework of the fractional coupled systems, a large number of researchers have conducted many research studies on the existence of solution for such a type of systems (for instances, see [19,20,21,22,23]). Obtaining the exact solutions of a non-linear boundary problem in the fractional settings is time-consuming wor,k and it is a task full of challenges
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