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
Solvability of Langevin equations with two Hadamard fractional derivatives via Mittag-Leffler functions
Maria Alessandra Ragusa
2021-01-01
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 resultsFile in questo prodotto:
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