Existence and Stability of a Caputo Variable-Order Boundary Value Problem
Amar Benkerrouche, Mohammed Said Souıd, Sumit Chandok, Ali Hakem
Abstract
In this study, we investigate the existence of a solution to the boundary value problem (BVP) of variable-order Caputo-type fractional differential equation by converting it into an equivalent standard Caputo (BVP) of the fractional constant order with the help of the generalized intervals and the piecewise constant functions. All our results in this study are proved by using Darbo’s fixed-point theorem and the Ulam–Hyers (UH) stability definition. A numerical example is given at the end to support and validate the potentiality of our obtained results.
Topics & Concepts
MathematicsPiecewiseConstant (computer programming)Variable (mathematics)Fixed-point theoremBoundary value problemStability (learning theory)Mathematical analysisConstant coefficientsOrder (exchange)Applied mathematicsDifferential equationEconomicsFinanceMachine learningProgramming languageComputer scienceFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisNumerical methods for differential equations