Solutions of certain initial-boundary value problems via a new extended Laplace transform

Abstract

In this article, we present a novel extended exponential kernel Laplace-type integral transform. The Laplace, natural, and Sumudu transforms are all included in the suggested transform. The existence theorem, Parseval-type identity, inversion formula, and other fundamental aspects of the new integral transform are examined in this article. Integral identities define the connections between the new transforms and the established transforms. In order to solve specific initial-boundary value problems, the new transforms are used.

Keywords

• laplace transform
• sumudu transform
• natural transform
• h-function
• h-transform
• inversion formula
• parseval-type identity
• borel–džrbashjan transform
• 44a10
• 44a20
• 33c20
• 33c60