Infinitesimal Prolongation for Fractional Derivative Ψ-Caputo Variable Order and Applications

In this work, we are concerned with the well-known Lie group theory to find symmetries of differential equations with fractional derivative Ψ -Caputo variable order. In this sense, we discuss the Leibniz-type rule and also the chain-type rule for the fractional derivative of this operator. In the en...

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Bibliographic Details
Published in:Qualitative theory of dynamical systems 2025, Vol.24 (1)
Main Authors: Soares, C. A., Costa, F. S., Sousa, J. Vanterler C.
Format: Article
Language:English
Subjects:
Derivatives
Difference and Functional Equations
Differential equations
Dynamical Systems and Ergodic Theory
Group theory
Lie groups
Mathematics
Mathematics and Statistics
Operators (mathematics)
Prolongation
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Summary:In this work, we are concerned with the well-known Lie group theory to find symmetries of differential equations with fractional derivative Ψ -Caputo variable order. In this sense, we discuss the Leibniz-type rule and also the chain-type rule for the fractional derivative of this operator. In the end, we apply the results obtained in the fractional Harry Dym-type equation to find its symmetries, and we present a solution for a fractional Harry Dym-type equation with constant order.
ISSN:1575-5460
1662-3592
DOI:10.1007/s12346-024-01157-y