Browsing by Author "Salimi, Mehdi"

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Citation Count: Singh, Jagdev...et al. (2021). "An efficient computational approach for local fractional Poisson equation in fractal media", Numerical Methods for Partial Differential Equations, Vol. 37, No. 2, pp. 1439-1448.
An efficient computational approach for local fractional Poisson equation in fractal media
(2021) Singh, Jagdev; Ahmadian, Ali; Rathore, Sushila; Kumar, Devendra; Baleanu, Dumitru; Salimi, Mehdi; Salahshour, Soheil; 56389
In this article, we analyze local fractional Poisson equation (LFPE) by employing q-homotopy analysis transform method (q-HATM). The PE describes the potential field due to a given charge with the potential field known, one can then calculate gravitational or electrostatic field in fractal domain. It is an elliptic partial differential equations (PDE) that regularly appear in the modeling of the electromagnetic mechanism. In this work, PE is studied in the local fractional operator sense. To handle the LFPE some illustrative example is discussed. The required results are presented to demonstrate the simple and well-organized nature of q-HATM to handle PDE having fractional derivative in local fractional operator sense. The results derived by the discussed technique reveal that the suggested scheme is easy to employ and computationally very accurate. The graphical representation of solution of LFPE yields interesting and better physical consequences of Poisson equation with local fractional derivative.
Citation Count: Kumar, Sunil...et al. (2020). "An Efficient Numerical Method for Fractional SIR Epidemic Model of Infectious Disease by Using Bernstein Wavelets", Mathematics, Vol. 8, No. 4.
An Efficient Numerical Method for Fractional SIR Epidemic Model of Infectious Disease by Using Bernstein Wavelets
(2020) Kumar, Sunil; Ahmadian, Ali; Kumar, Ranbir; Kumar, Devendra; Singh, Jagdev; Baleanu, Dumitru; Salimi, Mehdi; 56389
In this paper, the operational matrix based on Bernstein wavelets is presented for solving fractional SIR model with unknown parameters. The SIR model is a system of differential equations that arises in medical science to study epidemiology and medical care for the injured. Operational matrices merged with the collocation method are used to convert fractional-order problems into algebraic equations. The Adams-Bashforth-Moulton predictor correcter scheme is also discussed for solving the same. We have compared the solutions with the Adams-Bashforth predictor correcter scheme for the accuracy and applicability of the Bernstein wavelet method. The convergence analysis of the Bernstein wavelet has been also discussed for the validity of the method.