Solution of Specific Fractional Differential Equations by Natural Integral Transform

G. P. Kamble¹ , B. R. Sontakke²

Section:Research Paper, Product Type: Journal-Paper
Vol.6 , Issue.5 , pp.40-45, Oct-2019

CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i5.4045

Online published on Oct 31, 2019

Copyright © G. P. Kamble, B. R. Sontakke . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
In this paper, we apply the natural integral transform to some specific fractional differential equations which are easy to implement and are very effective and simple in performing a solution of the fractional differential equations. The solution was investigated in details with the help of natural integral transform. Here we apply natural integral transform to the fractional diffusion equation under external force, ∂^α/〖∂t〗^α u(x,t)=D ∂^2/〖∂t〗^2 u(x,t)-∂/∂t (f(x),u(x,t)),0<α≤1,D>0 Where u(x,t) represent the probability density function for finding a particle at the point x at the time instant t, the positive constant D depends on the temperature, the friction coefficient, the universal gas constant and finally on the Avogordo number f(x) are the external forces. The natural integral transform gives the solution of this diffusion equation which is in fractional form

Key-Words / Index Term :
Fractional derivative, Natural transform, Diffusion equation, Fractional differential equation, Homotopy perturbation method

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