Applications of Laplace Transform and Solution for Various Fractional Differential Equations

Abstract

Presently, many researchers have demonstrated the utility of fractional calculus in the derivation of
particular solutions of a considerably huge number of linear ordinary and partial differential equations of the second
and higher orders. Laplace decomposition technique is applied to achieve series solutions of nonlinear fractional
differential equation. The method is based mainly upon some general theorems on (explicit) particular solutions of some
families of fractional differential equations with the Laplace transform and the expansion coefficients of binomial series.
A major advantage of fractional calculus is that it can be considered as a super set of integer-order calculus. Thus,
fractional calculus has the potential to achieve what integer-order calculus cannot. It has been suppose that many of the
enormous future developments will come from the applications of fractional calculus to different fields. Laplace
transform is a very influential mathematical tool applied in various areas of engineering and science. With the
increasing complexity of engineering problems, Laplace transforms help in solving complex problems with a very
straightforward approach just like the applications of transfer functions to solve ordinary differential equations. It will
allow us to transform fractional differential equations into algebraic equations and then by solving these algebraic
equations. The unknown function by using the Inverse Laplace Transform can be o btained.