Solution of Abel’s Integral Equation by Modified Laplace Transform

Abstract

This paper provides a comprehensive and detailed analysis of the modified Laplace transform, exploring its applications in various mathematical and engineering domains. Initially, the modified Laplace transform is applied to various special functions including Mittag-Leffler function, k-Struve function, Bessel-Maitland function, and Generalized function. Following this, the study examines the modified Laplace transform of nth order derivative of a function. The paper also demonstrates how the modified Laplace transform can be utilized to solve Abel’s integral equation. Lastly, the research explores some practical applications of the modified Laplace transform in addressing real-world problems like chemical sciences and impulsive forces.