Hadamard functional fractional integrals and derivatives and fractional differential equations
K. Balachandran, Mohammed M. Matar, N. Annapoorani, D. Prabu
Abstract
This paper introduces a general type of new version of Hadamard fractional integrals and derivatives with respect to another function and studies some of their properties. Further, we prove the existence results for fractional differential equations with this Hadamard type fractional derivative. The results are established by applying the fixed point theorems. Examples are given to illustrate the theory.
Topics & Concepts
Hadamard transformMathematicsFractional calculusHadamard three-lines theoremType (biology)Pure mathematicsDifferential (mechanical device)Function (biology)Mathematical analysisApplied mathematicsHadamard productAerospace engineeringEngineeringBiologyEvolutionary biologyEcologyFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisFixed Point Theorems Analysis