ON GENERALIZED STIELTJES-TYPE INTEGRAL TRANSFORM: THEORY AND APPLICATIONS

Abstract

This paper is focused on the generalized Stieltjes-type integral transform. We derive the transform of a specific derivative operator and also achieve the transforms of integrals and fractional integrals. A significant contribution of this paper is the introduction of a new convolution associated with this transform, along with a proof of the corresponding convolution theorem. Additionally, the transform is employed to solve a variety of problems, including initial-boundary value problems for both ordinary and partial differential equations, as well as an integral equation. © 2025 Elsevier B.V., All rights reserved.