Abstract
In this paper we discuss the solvability of Langevin equations with two Hadamard fractional derivatives. The method of this discussion is to study the solutions of the equivalent Volterra integral equation in terms of Mittag–Leffler functions. The existence and uniqueness results are established by using Schauder's fixed point theorem and Banach's fixed point theorem, respectively. An example is given to illustrate the main results.
Acknowledgments
The second author wish to thank the support of ‘RUDN University Program 5-100’.
Disclosure statement
No potential conflict of interest was reported by the author(s).