Shodhganga Collection:
http://hdl.handle.net/10603/72766
Sat, 19 Oct 2019 21:57:56 GMT2019-10-19T21:57:56ZA Study of Fractional Calculus Operators and Integrals Pertaining to Certain Special Functions with Applications
http://hdl.handle.net/10603/230260
Title: 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.http://hdl.handle.net/10603/230260A Study of Fractional Calculus Operators and Integrals Pertaining to Certain Special Functions with Applications
http://hdl.handle.net/10603/72767
Title: 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.http://hdl.handle.net/10603/72767