Existence and Stability Results for Coupled System of Fractional Differential Equations Involving Ab-Caputo Derivative

Abstract

In this paper, we use Krasnoselskii’s fixed point theorem to find existence results for the solution of the following nonlinear fractional differential equations (FDEs) for a coupled system involving AB-Caputo fractional derivative [Formula: see text] with boundary conditions [Formula: see text] We discuss uniqueness with the help of the Banach contraction principle. The criteria for Hyers–Ulam stability of given AB-Caputo fractional-coupled boundary value problem (BVP) is also discussed. Some examples are provided to validate our results. In Example 1, we find a unique and stable solution of AB-Caputo fractional-coupled BVP. In Example 2, the analysis of approximate and exact solutions with errors of nonlinear integral equations is elaborated with graphs.

Solvability, Approximation and Stability of Periodic Boundary Value Problem for a Nonlinear Hadamard Fractional Differential Equation with p-Laplacian

“…Subsequently, extensive and in-depth research was conducted on the Ulam-Hyers stability of various systems. Especially, many excellent research results have emerged regarding the Ulam-Hyers stability of fractional order differential systems (see some of them [3,21,[24][25][26][27][28][29][30][31][32]). Moreover, it is rare to combine the Hadamard fractional derivative with Laplacian operator.…”

Fractional order mathematical modeling of lumpy skin disease

“…The Caputo derivative serves best as a base model and is preferred over Riemann-Liouville fractional derivative for formulating epidemiological models for the obvious reasons concerning the use of initial and boundary conditions and the differentiation of a constant being zero. For more details one can refer to the following researches [4], [7], [8], [18], [20], [23], [25], [26], [36], [40], [47], [52], [54], [58], [62].…”