Analytical Solutions for Time-Fractional Cauchy Reaction-Diffusion Equations Using Iterative Laplace Transform Method

Abstract

In the present work, the iterative Laplace transform method (ILTM) is implemented to derive approximate analytical solutions for the time-fractional Cauchy reaction-diffusion equations (CRDEs) within the Caputo fractional derivative. The proposed technique is an elegant amalgam of the Iterative method and the Laplace transform method. The ILTM produces the solution in a rapid convergent series which may lead to the solution in a closed form. The obtained analytical outcomes with the help of the proposed technique are examined graphically.

An Efficient Analytical Technique for Solving Newell-Whitehead-Segel Equations of Fractional Order

“…Substituting the results from equations ( 12) to (14) in the equation (36) and applying the equations ( 16) to (18), we determine the components of the ILTM solution as follows 0 ( , ) ,…”

“…Jafari et al have made elegant use of Laplace transform in this iterative method and it became a popular method known as iterative Laplace transform method (ILTM) [8] to examine a system of partial differential equations of fractional order. Recently, ILTM has been used to solve fractional Fokker-Plank equations [9], fractional Telegraph equations [10], fractional Schrödinger equations [11], fractional heat and wave like equations [12], fractional Navier-Stokes equations [13], and fractional Cauchy reaction-diffusion equations [14], etc.…”

Analytical Approach for Solving Space-Time Gas Dynamic Equations of Fractional Order Via Laplace transform

“…Recently, Jafari et al [21] suggested an innovative direct method, termed the iterative Laplace transform method (ILTM), for finding numerical solutions to a system of fractional partial differential equations by employing the Laplace transform in the iterative method. More recently, fractional Fokker-Planck equations [22] , fractional telegraph equations [23] , fractional Schrödinger equations [24] , fractional heat and wave like equations [25] , fractional Navier-Stokes equations [26] , fractional Cauchy reaction-diffusion equations [27] , and fractional Newell-Whitehead-Segel equations [28] have been solved by the ILTM.…”