Unification of integral transforms and their applications

Abstract

An integral transform called BA-transform is introduced in this work, which yields a known number of transforms by changing variables. We prove that Laplace, Sumudu, Natural, Elzaki, Aboodh, Tarig, Srivastava, Kamal, Laplace–Carson, Mohand, Shehu and Sawi transforms are the particular cases of our new generalized integral transform. We establish for our transform few fundamental properties, connections with these well-known integral transforms in literature and some test examples with their graphic illustrations in application section. Also, the double new integral transform and some of its fundamental properties are investigated. Some results and relationships between our simple and double integral transforms are also established.

Keywords

• B-transform
• BA-transform
• BB-transform
• Differential equations
• Partial differential equations