INTRODUCING THE UPADHYAYA INTEGRAL TRANSFORM

Abstract

Through this introductory paper we announce to the worldwide mathematics community a new type of integral transform, which we call the Upadhyaya Integral Transform or, the Upadhyaya transform (UT), in short. The new transform which we propose to proclaim through this paper, is, in fact a generalized form of the celebrated Laplace transform. The power of this generalization is that this most general form of the Laplace transform generalizes and unifies, besides the classical Laplace transform and the Laplace-Carson transform, most of the very recently introduced integral transforms of this category like, the Sumudu transform, the Elzaki transform, the Kashuri and Fundo transform, the Mahgoub transform,  the ZZ- transform, the Sadik transform, the Kamal transform, the Natural transform, the Mohand transform, the Aboodh transform, the Ramadan Group transform, the Shehu transform, the Sawi transform, the Tarig transform, the Yang transform, etc.  We develop the general theory of the Upadhyaya transform in a way which exactly parallels the existing theory of the classical Laplace transform and also provide a number of possible generalizations of this transform and thus we prepare a firm ground for future researches in this field by employing this most generalized, versatile and robust form of the classical Laplace transform – the Upadhyaya transform –  in almost all  the areas wherever, the classical Laplace transform and its various aforementioned variants are currently being employed for solving the vast multitude of problems arising in the areas of applied mathematics, mathematical physics and  engineering sciences and other  possible fields of study inside and outside the realm of mathematics.