A Study of Generalized Riemann Liouville Operators and their Applications

Abstract

One of the classical streams of Mathematics is Fractional Calculus which is connected to the study of Fractional order integrals as well as derivative operators which encompasses both the domains be it real or complex. This study also comprises their applications in the associated fields. The fundamentals of Fractional Calculus (Fractional derivatives and Fractional integrals) are quite traditional. A Fractional derivative may be simply defined as an operator, the function of which is to generalize an ordinary derivative. Fractional differential equations that have involved both the real and the complex order derivatives definitely have created a niche for modelling the unusual dynamics of several processes that have relation with complex systems in the areas of engineering as well as science. Fractional calculus may be considered as generalization of conventional calculus due to the fact that it extends the concept of the derivatives and integrals to cater to the arbitrary orders. This report aims first to expose the concepts, applicable definitions of Fractional Calculus Operators, Special Functions, Generalized Fractional Calculus and second to demonstrate how these functions are used for solving several Fractional differential equations along with their applications in diverse areas. The main objective of thesis is to examine and investigate the generalized Fractional Operators and the composition of Special Functions with them newline