Study of Some Integral Transforms and their Applications

Abstract

Differential equation is the branch of Mathematics which plays an vital role newlinein Mathematical sciences and Engineering field. There are various traditional newlinemethods for solving Ordinary and Partial differential equations. Integral transforms newlinelike Fourier, Laplace, Sumudu, Elzaki, etc. are tools which are convenient to solve newlinedifferential equations with initial conditions. newlineIn this work initially we have studied some integral transforms such as newlineLaplace, Sumudu and Elzaki with their comparison in solving Ordinary differential newlineequations with variable coefficients. In the second part we have presented newlineapplications of these integral transforms in the process of Cryptography and newlinegeneralized some results which will be helpful for secured communication. newline2 Objectives: newlineThe main objectives of the study carried out are stated below. newline(i)To Study and understand some integral transforms such as L.T., S.T., E.T. with newlinetheir properties and applications newline(ii)To compare S.T. with L.T. and E.T. and sort out some similarities and differences newlinein solving O.D.E.with variable coefficients. newline(iii)To study one interesting and useful application of L.T. in the process of newlinecryptography and to find out some new generalizations. newline(iv)To apply new integral transforms Sumudu and Elzaki in the process of newlinecryptography and find some more generalizations applicable in society newline(particularly for scientists, engineers, industrialists etc.) newlineiii newline3 Proposed Contents and Brief Description of The Thesis: newlineThe thesis entitled Study of Some Integral Transforms and their newlineApplications has six chapters and each chapter is divided into sections and newlinesubsections .The chapter wise scheme of the thesis is given below newline