In a series of papers, we discussed the solution of Laplace’s differential equation (DE) by using fractional calculus, operational calculus in the framework of distribution theory, and Laplace transform. The solutions of Kummer’s DE, which are expressed by the confluent hypergeometric functions, are obtained with the aid of the analytic continuation (AC) of Riemann–Liouville fractional derivati...

This paper, for the first time ever, proposes a Laplace-like integral transform, which is called as He-Laplace its basic properties are elucidated. The homotopy perturbation method coupled with this new transform becomes much effective in solving fractal differential equations. Phi-four equation He?s derivative used an example to reveal main merits of present technology.

Fundamental solutions of dynamic poroelasticity and generalized thermoelasticity are derived in the Laplace transform domain. For poroelasticity, these solutions define the solid displacement field and the fluid pressure in fluid-saturated media due to a point force in the solid and an injection of fluid in the pores. In addition, approximate fundamental solutions for short times are derived by...