A note on a class of Caputo fractional differential equations with respect to another function
Zaky M.A. Hendy A.S. Suragan D.
June 2022Elsevier B.V.
Mathematics and Computers in Simulation
2022#196289 - 295 pp.
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.
Analytical solution , Existence and uniqueness , Fractional derivative with respect to another function , Variable-order derivative , Well-posedness
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Department of Mathematics, Nazarbayev University, Nur-Sultan, Kazakhstan
Department of Applied Mathematics, National Research Centre, Dokki, Cairo, 12622, Egypt
Department of Computational Mathematics and Computer Science, Institute of Natural Sciences and Mathematics, Ural Federal University, 19 Mira St., Yekaterinburg, 620002, Russian Federation
Department of Mathematics
Department of Applied Mathematics
Department of Computational Mathematics and Computer Science
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