Existence and Stability of a Caputo Variable-Order Boundary Value Problem | Zendy

Amar Benkerrouche | Zendy; Mohammed Said Souıd | Zendy; Sumit Chandok | Zendy; Ali Hakem | Zendy

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Existence and Stability of a Caputo Variable-Order Boundary Value Problem

Author(s) -

Amar Benkerrouche,

Mohammed Said Souıd,

Sumit Chandok,

Ali Hakem

Publication year - 2021

Publication title -

journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.252

H-Index - 13

eISSN - 2314-4785

pISSN - 2314-4629

DOI - 10.1155/2021/7967880

Subject(s) - mathematics , piecewise , constant (computer programming) , variable (mathematics) , fixed point theorem , boundary value problem , stability (learning theory) , mathematical analysis , constant coefficients , order (exchange) , differential equation , finance , machine learning , computer science , economics , programming language

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.

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