contribution to fractional mathematical analysis and Special functions with applications

Abstract

The thesis has been divided into six chapters. Besides the introductory first chapter, newlinesecond chapter deals with the study of certain properties viz. differential recurrence relations, newlinedifferential equation and Rodrigue s formula of some well-known orthogonal polynomials newlineusing results concerning eigenvector for the product of two operators defined on a Lie algebra newlineof endomorphisms of a vector space. Third chapter concerns with study of fractional newlineintegral formulae and integral transforms formulae of extended hypergeometric functions newlinehas recently been introduced by Luo et al. [155]. Also we introduced new integral transforms newlineinvolving extended hypergeometric functions and established their inversion theorems. newlineParseval-Goldstein type relations for the newly-introduced integral transforms are also been newlinepresented. Classical integral transforms, such as Laplace, Stieltjes and Widder-Potential are newlineseen to follow as special cases of the newly-introduced integral transforms. In fourth chapter, newlinewe introduced a new concept of functions of bounded fractional differential variation using newlinethe Caputo fractional derivatives. It is proved that the space of functions of bounded fractional differential variation on [a,b] is a normed algebra under certain type of norms. In second last chapter, we introduce generalized iterative method to solve linear and nonlinear fractional differential equations with composite fractional derivative operator. Linear/nonlinear fractional diffusion-wave equations, time-fractional diffusion equation, time fractional Naviour-Stoke equation have been solved using generalized iterative method. In last chapter, we study fractional modeling of certain physical systems viz. temperature distribution and heat flux in the semi infinite solid, heat transfer through diathermanous materials, temperature distribution within a spinning satellite and flow of electric current in R-L circuit. We also introduced generalized fractional kinetic equations involving generalized Lommel-Wright functions. We also obtained an