A New Integral Transform “Rishi Transform” with Application

Abstract

In this paper, authors propose a new integral transform “Rishi Transform” with application to determine the exact (analytic) solution of first kind Volterra integral equation (V.I.E.). For this purpose, authors first derived the Rishi transform of basic mathematical functions (algebraic and transcendential) and then the fundamental properties of Rishi transform is discussed, which can be used for solving ordinary differential equations (O.D.E), partial differential equations (P.D.E.), delay differential equations (D.D.E.), fractional differential equations (F.D.E.), difference equations (D.E.), integral equations (I.E.) and integro-differential equations (I.D.E.).  After this, authors determined the exact (analytic) solution of general first kind V.I.E.. They have considered three numerical problems and solved them completely step by step for explaining the utility of Rishi transform. Results depict that the proposed new integral transform "Rishi Transform" provides the exact results for first kind V.I.E. without doing complicated calculation work.