Boundary Value Problems of Hadamard Fractional Differential Equations of Variable Order

A boundary value problem for Hadamard fractional differential equations of variable order is studied. Note the symmetry of a transformation of a system of differential equations is connected with the locally solvability which is the same as the existence of solutions. It leads to the necessity of obtaining existence criteria for a boundary value problem for Hadamard fractional differential equations of variable order. Also, the stability in the sense of Ulam-Hyers-Rassias is investigated. The results are obtained based on the Kuratowski measure of noncompactness. An example illustrates the validity of the observed results.

Automated summary

This paper investigates a boundary value problem for Hadamard fractional differential equations of variable order, exploring the connection between the symmetry of transformations and local solvability, and examining the existence criteria and stability in the sense of Ulam-Hyers-Rassias. The results are obtained based on the Kuratowski measure of noncompactness, with an example illustrating the validity of the observed results.