Department of Mathematics

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Adomian decomposition and homotopy perturbation method for the solution of time fractional partial integro-differential equations
(Springer, 2021-07) Santra, Sudarshan
This article deals with two different methods to solve a time fractional partial integro-differential equation. The fractional derivatives are defined here in Caputo sense. The model problem is solved using the Adomian decomposition method and homotopy perturbation method. Moreover, this paper proves the convergence analysis of the solution based on the present methods. Numerical evidences are illustrated in support of the theoretical analysis.
Numerical treatment of multi-term time fractional nonlinear KdV equations with weakly singular solutions
(Taylor & Francis, 2021-12) Santra, Sudarshan
The main aim of this work is to construct an efficient recursive numerical technique for solving multi-term time fractional nonlinear KdV equation. The fractional derivatives are defined in Caputo sense. A modified Laplace decomposition method is introduced to approximate the solution. The Adomian polynomials play an important role to execute such a recursive process. In addition, the mathematical importance and some applications of KdV equation are discussed. The approximate solution obtained by the proposed method can be expressed in the form of an infinite convergent series. The experimental evidences demonstrate the effectiveness of the proposed method.