Dr. RISHI KUMAR PANDEY
@modyuniversity.ac.in
Assistant Professor
Mody University of Science and Technology
RESEARCH INTERESTS
Fractional Calculus, Numerical Analysis, Partial Differential Equations
Scopus Publications
Scholar Citations
Scholar h-index
Scholar i10-index
Scopus Publications
Abhijeet K. Digalwar, Sudhanshu Ranjan Singh, Rishi Pandey, and Ankur Sharma
Springer Nature Switzerland
Hradyesh Kumar Mishra and Rishi Kumar Pandey
Springer Science and Business Media LLC
In this paper, a semi-analytic solution of time-fractional nonlinear dispersive type of the Zakharov–Kuznetsov (ZK) equations is obtained by the means of homotopy analysis fractional Sumudu transform method. Several examples are evaluated and compared with exact solutions to show the effectiveness of arbitrary order of ZK equations. The results demonstrate that the method is highly reliable and convenient to apply and evaluate without restrictions like finite domain, finite discretization or perturbation of small and large physical parameters.
Rishi Kumar Pandey and Hradyesh Kumar Mishra
Elsevier BV
Abstract In this paper, the semi-analytic numerical technique for the solution of time-space fractional telegraph equation is applied. This numerical technique is based on coupling of the homotopy analysis method and sumudu transform. It shows the clear advantage with mess methods like finite difference method and also with polynomial methods similar to perturbation and Adomian decomposition methods. It is easily transform the complex fractional order derivatives in simple time domain and interpret the results in same meaning.
Rishi Kumar Pandey and Hradyesh Kumar Mishra
Springer Science and Business Media LLC
In this article, we apply the newly introduced numerical method which is a combination of Sumudu transforms and Homotopy analysis method for the solution of time fractional third order dispersive type PDE equations. It is also discussed generalized algorithm, absolute convergence and analytic result of the finite number of independent variables including time variable.
Rishi Kumar Pandey and Hradyesh Kumar Mishra
Walter de Gruyter GmbH
AbstractThe time and space fractional wave and heat type equations with variable coefficients are considered, and the variable order derivative in He‘s fractional derivative sense are taken. The utility of the homotopy analysis fractional sumudu transform method is shown in the form of a series solution for these generalized fractional order equations. Some discussion with examples are presented to explain the accuracy and ease of the method.