Generalization of Fractional Calculus Operators With Applications: Developments

Abstract

In this paper the operators of fractional calculus are generalized, that is generalization of the classical Riemann- Liouvelli (RL) fractional integral, and of the RL and Caputo’s fractional derivatives. As further generalization the fractional integral and fractional derivatives are defined with respect to base function along with weights, and properties of these generalized operators are derived. The generalization of fractional calculus also gives several other types of fractional order operators like Hadamard, Riesz, Erdelyi Kober, by choice of kernel, the weight and base function. This development of generalization is useful in the context of optimization problems of fractional calculus of variation; and also useful in solving a set of integral equations, those are demonstrated in this paper.