A New Integral Transform “Rishi Transform” with Application
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.
How to Cite
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
© Journal of Scientific Research
Articles published in the "Journal of Scientific Research" are Open Access articles under a Creative Commons Attribution-ShareAlike 4.0 International license (CC BY-SA 4.0). This license permits use, distribution and reproduction in any medium, provided the original work is properly cited and initial publication in this journal. In addition to that, users must provide a link to the license, indicate if changes are made and distribute using the same license as original if the original content has been remixed, transformed or built upon.