Existence and Stability of Solutions to Differential Equations via the Deformable Derivative and Laplace Transform

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Abstract

In this short note, we establish the Existence and stability of solutions of an abstract semilinear differential equation governed by the so-called deformable derivative. We achieve our results using Banach’s contraction principle, the Laplace transform, and the Gronwall inequality. These results are new in the context of fractional differential equations.

Keywords:

Deformable derivative Fractional differential equations Banach’s contraction principle

Author Biographies

  • Mesfin M. Etefa

    NEERLab Laboratory, Department of Mathematics, Bowie State University, 14000 Jericho Park Rd., Bowie, MD 20715, USA

  • Gaston M. N’Guérékata

    University Distinguished Professor, NEERLab Laboratory, Department of Mathematics, Morgan State University, 1700 E. Cold Spring Lane, Baltimore, M.D. 21251, USA

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DOI

10.4208/ajiam.2025-0008

How to Cite

Existence and Stability of Solutions to Differential Equations via the Deformable Derivative and Laplace Transform. (2025). African Journal for Industrial and Applied Mathematics. https://doi.org/10.4208/ajiam.2025-0008