TY - JOUR
T1 - A note on a class of Caputo fractional differential equations with respect to another function
AU - Zaky, M. A.
AU - Hendy, A. S.
AU - Suragan, D.
N1 - Funding Information:
The authors are grateful to the handling editor and the anonymous referees for their constructive feedback and helpful suggestions, which highly improved the presentation of the paper. D. Suragan and Mahmoud A. Zaky were funded by the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan (Grant No. AP09058317 ). Mahmoud A. Zaky is also supported by the National Research Centre of Egypt and Nazarbayev University program 091019CRP2120 . Ahmed S. Hendy wishes to acknowledge the support of the RSF grant, project 22-21-00075.
Publisher Copyright:
© 2022 International Association for Mathematics and Computers in Simulation (IMACS)
PY - 2022/6
Y1 - 2022/6
N2 - 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.
AB - 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.
KW - Analytical solution
KW - Existence and uniqueness
KW - Fractional derivative with respect to another function
KW - Variable-order derivative
KW - Well-posedness
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U2 - 10.1016/j.matcom.2022.01.016
DO - 10.1016/j.matcom.2022.01.016
M3 - Article
AN - SCOPUS:85124422295
SN - 0378-4754
VL - 196
SP - 289
EP - 295
JO - Mathematics and Computers in Simulation
JF - Mathematics and Computers in Simulation
ER -