Resumen de Infinitesimal Prolongation for Fractional Derivative 9-Caputo Variable Order and Applications

C.A. Soares Jr, F.S. Costa, J. Vanterler da C. Sousa

• 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.