Shankar Raut - Academia.edu (original) (raw)

Shankar Raut

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Papers by Shankar Raut

In this paper, we develop Implicit and Crank-Nicolson finite difference scheme for time fractiona... more In this paper, we develop Implicit and Crank-Nicolson finite difference scheme for time fractional radon diffusion equation. We discuss the stability and convergence of both the scheme. As an application of this scheme, we obtain the numerical solutions of the test problem and represented graphically by mathematical software Mathematica and finally, we compare the rate of convergence of both the scheme. Index Terms – Fractional calculus, Explicit Finite difference, Caputo formula, Stability, Convergence.

$Research paper thumbnail of Analytical Solution of Linear Fractional Partial Dierential Equation of Order 0 $<$ $\alpha$ $\leq$1$

Journal of Advances in Mathematics and Computer Science

The paper aims to obtain exact analytical solution of linear nonhomogeneous space-time fractional... more The paper aims to obtain exact analytical solution of linear nonhomogeneous space-time fractional order partial differential equation by improved Adomian decomposition method coupled with fractional Taylor expansion series. The solution of these equations are in series form may have rapid convergence to a closed-form solution. The effectiveness and sharpness of this method is shown by obtaining the exact solution of these equations with suitable initial conditions (ICs). With the help of this method, it is possible to investigate nature of solutions when we vary order of the fractional derivative. Behaviour of the solution of these equations are represented by graphs using Matlab software.

$Research paper thumbnail of Analysis of fractional Kawahara and modified Kawahara equations based on Caputo-Fabrizio derivative operator$

Journal of Mathematical and Computational Science, 2021

In this paper, nonlinear time fractional Kawahara and modified Kawahara equations based on Caputo... more In this paper, nonlinear time fractional Kawahara and modified Kawahara equations based on Caputo-Fabrizio derivative operator is analysed using iterative Laplace transform method to obtain approximate solutions. The substantive features of the manuscript is to offer the stability conditions of solution for proposed technique. The acquired approximate solutions are in comparison with the precise solutions to confirm the applicability, performance and accuracy of the method. Moreover, the 3D plots of obtained numerical solution of the concerned equations for various specific cases are presented.