Nonlocal initial value problems for implicit differential equations with Hilfer–Hadamard fractional derivative - Vivek, Devaraj; Kanagarajan, Kuppusamy; Elsayed, Elsayed M. M. (Nonlinear Analysis: Modelling and Control, 2018)
In this paper, the Schaefer's fixed-point theorem is used to investigate the existence of solutions to nonlocal initial value problems for implicit differential equations with Hilfer–Hadamard fractional derivative. Then the Ulam stability result is obtained by using Banach contraction principle. An example is given to illustrate the applications of the main result.
Keywords: Hilfer–Hadamard fractional derivative; implicit differential equations; fixed point; generalized Ulam–Hyers stability