On Certain Volterra-Type Integral Equations Involving k, p − k and p, s, k Mittag–Leffler Functions

Abstract

In the present paper, we investigate three theorems of the Volterra type containing \(k, p-k\) and \(p,s,k\) Mittag–Leffler functions. Moreover, the Laplace transforms of the \(k, p-k\) and \(p,s,k\) Mittag–Leffler functions are derived here. The solutions to these problems were obtained by the Laplace transform method. In some special cases, new and known results are also obtained here. The acquired results are suitable in the fields of applied science, physics, engineering, and technology. The novelty of this work lies in their enhanced modeling capabilities, improved solution methods, and interdisciplinary applicability, making them a powerful tool for understanding complex systems across various fields. Also, the special function involved here can be reduced to simple functions; those have a variety of applications in different areas of science and technology. In the future, researchers can do more work on Volterra-type integrals and differential equations using various types of special functions.