Analytic solutions for singular integral equations and non-homogeneous fractional PDE

In the last three decades, transform methods have been used for solving fractional di erential equations, singular integral equations. In this article, the author considered a new class of the inverse Laplace transforms of exponential types. We also evaluated certain types of integrals and solved partial fractional equations of Cauchy type.The result reveals that the transform method is very convenient and e ective