Ulam type stability of \(\psi \)-Riemann-Liouville fractional differential equations using \(\left( k,\psi \right) \)-generalized Laplace transform

Volume 17, Issue 2, pp 100--114 https://dx.doi.org/10.22436/jnsa.017.02.03

Publication Date: May 31, 2024 Submission Date: November 21, 2023 Revision Date: December 10, 2023 Accteptance Date: December 26, 2023

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Authors

A. Mısır - Department of Mathematics, Faculty of Sciences, Gazi University, Ankara, Turkey. E. Cengizhan - Department of Mathematics, Graduate School of Natural and Applied Sciences, Gazi University, Ankara, Turkey. Y. Başcı - Department of Mathematics, Faculty of Art and Sciences, Bolu Abant Izzet Baysal University, Bolu, Turkey.

Abstract

The primary objective of this paper is to explore the Hyers-Ulam stability of the \(\psi \)-Riemann-Liouville fractional differential equations by employing the \((k,\psi )\)-generalized Laplace transform method. The outcomes of our investigation represent advancements over certain existing results in the literature. Furthermore, we present illustrative examples to elucidate our primary findings.

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Keywords

• Hyers-Ulam stability
• Riemann-Liouville fractional derivative
• linear differential equation
• \(\left( k,\psi \right) \)-generalized Laplace transform

MSC

•  34K20
•  26D10
•  44A10
•  26A33
•  33B15

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