A Study of Fractional Calculus Operators and Integrals Pertaining to Certain Special Functions with Applications

Abstract

The subject matter presented in the thesis has been divided into twelve chapters. The first chapter gives an introduction to the topic of our study and a brief survey of the contributions made by earlier workers on the subject matter presented in the thesis. The second chapter gives a brief description of the survey and review of the literature carried out towards accomplishment of the research work. The third chapter is devoted to the study of a pair of unified and extended fractional integral operators involving the multivariable H-Function, Fox s H-Function and general class of polynomials. In the Fourth chapter, we study and develop the images of the generalized fractional integral operators given by Saigo in terms of the product of I-function and general class of polynomials. In the fifth chapter, we discuss the N-fractional calculus of product of a general class of functions with I-function and and#119867;and#773; - Function. In the Sixth chapter, certain integrals involving product of the I- function and Fox - Wright s Generalized Hypergeometric Function have been established. In the seventh chapter we establish three integrals and three theorems involving Srivastava s Polynomials and Aleph (and#8501;)- Function. In the Eigth chapter, we evaluate a general class of multiple Eulerian integral with integrands involving a product of general class of polynomials, a general sequence of functions and the multivariable H-function with general arguments. In the Ninth chapter, we present a comparative study of applications of Laplace Transform and Sumudu transform to and#119919;and#773;- function. In the Tenth chapter a Mathematical Model and its result involving the I -Function is presented to study the effect of environmental pollution on the growth and existence of Biological Populations. In Chapter eleven, in brief, we discuss the results obtained in accordance of the objectives set. The twelfth chapter contains the summary and conclusions of the work carried out during the course of study.