HADAMARD FRACTIONAL CALCULUS ON TIME SCALES
Ting-Ting Song, Guo–Cheng Wu, Jia-Li Wei
Abstract
This study defines a Hadamard fractional sum by use of the time-scale theory. Then a [Formula: see text]-fractional difference is given and fundamental theorems are proved. Initial value problems of fractional difference equations are presented and their equivalent fractional sum equations are provided. The discrete Mittag-Leffler function solutions of linear fractional difference equations are obtained. It can be concluded that the new discrete fractional calculus of Hadamard type is well defined.
Topics & Concepts
Hadamard transformFractional calculusMathematicsTime-scale calculusHadamard three-lines theoremType (biology)Function (biology)Mittag-Leffler functionApplied mathematicsMathematical analysisCalculus (dental)Hadamard productMultivariable calculusEngineeringControl engineeringBiologyDentistryMedicineEcologyEvolutionary biologyFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisIterative Methods for Nonlinear Equations