Dualities between ''Kamal & Mahgoub Integral Transforms'' and ''Some Famous Integral Transforms''
Nidal E. Hassan Taha *
Department of Mathematics, Faculty of Sciences and Arts-Almikwah, Albaha University, Saudi Arabia
R. I. Nuruddeen
Department of Mathematics, Faculty of Science, Federal University Dutse, Jigawa State, Nigeria
Abdelilah Kamal H. Sedeeg
Department of Mathematics, Faculty of Sciences and Arts-Almikwah, Albaha University, Saudi Arabia and Department of Mathematics, Faculty of Education, Holy Quran and Islamic Studies University, Sudan.
*Author to whom correspondence should be addressed.
Abstract
Abdelilah Kamal and Mohand Mahgoub recently introduced new integral transforms separately by the names the “Kamal transform” and “Mahgoub transform” to facilitate the solution of differential and integral equations. However, in this paper, these newly introduced integral transforms will closely be studied in relation to the some existing famous integral transforms defined in the time domain. The study will also try to establish the duality relations existing between these new integral transforms and in particular, the Laplace, Sumudu, Elzaki and Aboodh integral transforms. Further, supporting illustrations obtained from some test functions as examples are will be presented.
Keywords: Kamal, Mahgoub, Aboodh, Elzaki, Sumudu, Laplace transforms