Solvability of Langevin equations with two Hadamard fractional derivatives via Mittag–Leffler functions
Mohamed I. Abbas, Maria Alessandra Ragusa
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.
Topics & Concepts
MathematicsFixed-point theoremHadamard transformUniquenessBanach fixed-point theoremFractional calculusHadamard three-lines theoremMittag-Leffler functionPicard–Lindelöf theoremVolterra integral equationPure mathematicsSchauder fixed point theoremBanach spaceMathematical analysisApplied mathematicsIntegral equationHadamard productFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisDifferential Equations and Boundary Problems