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

Abstract

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