Journal
FRACTAL AND FRACTIONAL
Volume 6, Issue 2, Pages -Publisher
MDPI
DOI: 10.3390/fractalfract6020051
Keywords
variable order fractional calculus; existence-uniqueness; continuation theorem; Ulam-Hyers stability
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Funding
- Deanship of Scientific Research (DSR) at King Fahd University of Petroleum & Minerals (KFUPM), Kingdom of Saudi Arabia
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In this article, we investigate a Caputo type variable order fractional differential equation, discussing the existence-uniqueness, continuity and global existence of the solution. Moreover, we present a novel study on Ulam-Hyers stability of the equation.
In the theory of differential equations, the study of existence and the uniqueness of the solutions are important. In the last few decades, many researchers have had a keen interest in finding the existence-uniqueness solution of constant fractional differential equations, but literature focusing on variable order is limited. In this article, we consider a Caputo type variable order fractional differential equation. First, we present the existence-uniqueness of a solution of the considered problem. Secondly, By borrowing the idea from the theory of ordinary differential equations, we extend the continuation theorem for the variable order fractional differential equation. Further, we prove the global existence results. Finally, we present different types of Ulam-Hyers stability results, which have never been studied before for the Caputo type variable order fractional differential equation.
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