Paper Details

Presently, many researchers have demonstrated the utility of fractional calculus in the derivation ofparticular solutions of a considerably huge number of linear ordinary and partial differential equations of the secondand higher orders. Laplace decomposition technique is applied to achieve series solutions of nonlinear fractionaldifferential equation. The method is based mainly upon some general theorems on (explicit) particular solutions of somefamilies 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 theenormous future developments will come from the applications of fractional calculus to different fields. Laplacetransform is a very influential mathematical tool applied in various areas of engineering and science. With theincreasing complexity of engineering problems, Laplace transforms help in solving complex problems with a verystraightforward approach just like the applications of transfer functions to solve ordinary differential equations. It willallow us to transform fractional differential equations into algebraic equations and then by solving these algebraicequations. The unknown function by using the Inverse Laplace Transform can be o btained.

Dr. Saroj Choudhary, “Applications of Laplace Transform and Solution for Various Fractional Differential Equations”, International Journal of Advance Engineering and Research Development (IJAERD), Vol. 2, Issue 5, pp. 1372-1376, May 2015.