A note on a class of Caputo fractional differential equations with respect to another function

M.A. Zaky, A.S. Hendy and D. Suragan

Mathematics and Computers in Simulation (MATCOM), 2022, vol. 196, issue C, 289-295

Abstract: The mathematical analysis and solutions for a class of ψ-Caputo fractional differential equations are discussed. Assuming that ψ(t) is strictly monotone and armed by the possibility of converting the ψ-Caputo fractional differential equations with respect to another function ψ to its Caputo counterpart by a mapping transformation, the solutions of the ψ-Caputo fractional differential equations can be deduced from the solution representation for the Caputo version via an inverse transformation. We show that the mapping transformation for such derivatives is extremely useful in practical applications. The representation of solutions for constant order time ψ-Caputo fractional diffusion equation and variable order ψ-Caputo fractional mobile-immobile diffusion equation is investigated and the regularity estimates are deduced accordingly.

Keywords: Fractional derivative with respect to another function; Well-posedness; Existence and uniqueness; Variable-order derivative; Analytical solution (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:196:y:2022:i:c:p:289-295

DOI: 10.1016/j.matcom.2022.01.016

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