Study of Fractional Calculus and Integral Transform on Special Functions and Their Applications

Abstract

newlineThe subject matter presented in the thesis has been divided into seven 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 it also gives a brief description of the survey and review of the literature carried out towards accomplishment of the research work. The second chapter is devoted to the study of the composition of Pathway Fractional Integral Operator and the generalized K Wright function. This fractional operator is put in an application to the power multiples of generalized K Wright function and the results are obtained in the terms generalized K Wright function of higher order.In the Third chapter, we study and develop the new and interesting results of the Marichev Saigo Maeda Fractional Differential Operators on Generalized k-Struve function and on generalizedfunction.The results are obtained in the terms of generalized Wright Hypergeometric function, and Generalized Hyper geometric function.In the fourth chapter, we discuss the formulas of Marichev Saigo Maeda fractional operators pertaining to the p-k extended Mittag-Leffler function and applications as special cases. In the fifth chapter, certain integrals transform, including Euler transform, Laplace transform, Whittaker transform, K-transform, and Fractional Fourier transform of special function and K4-functionhave been establishedin terms of Generalized Wright function and further these results are expressed in terms of Generalized Hypergeometric function.In the sixth chapter, we establish certain image formulas using Pathway fractional integral operators with the properties of generalized function. The seventh chapter contains the summary and conclusions of the work carried out during the course of study.Finally, a list of publications contributed by the author having a bearing on the subject matter of the present work is attached followed by the reprints of the published work. newline newline newline