• HODA F AHMED

Articles written in Pramana – Journal of Physics

• Analytical approaches to space- and time-fractional coupled Burgers’ equations

We solve the one- and two-dimensional fractional coupled Burgers’ equations (FCBEs) by three different methods. The proposed methods are the Laplace–Adomian decomposition method (LADM), the Laplace-variational iteration method (LVIM) and the reduced differential transform method (RDTM). The solutions are obtained as rapidly convergent series with simply calculable terms. Numerical studies of the application of theseapproaches for a number of sample problems are given and are illustrated graphically. With these methods, it is possible to investigate the nature of solutions when the fractional derivative parameters are changed. The numerical results reveal the effectiveness and the correctness of the proposed methods.

• Numerical study of multidimensional fractional time and space coupled Burgers’ equations

This paper declares a new spectral collocation technique to provide accurate approximate solutions of the one- and two-dimensional time and space fractional coupled Burgers’ equations (TSFCBEs) in which the fractional derivatives are defined according to Caputo’s definition. The suggested method is based on the shifted Gegenbauer polynomials (SGPs) for approximating the solution of TSFCBEs. The suggested technique reduces the considered problems to the solution of nonlinear algebraic equations (NLAEs). Moreover, the accuracy and reliability of the proposed method are confirmed through numerical examples. Finally, the obtained numerical results are compared with those previously reported in the literature.

• Correction to: Analytical approaches to space- and time-fractional coupled Burgers' equations

• Gegenbauer spectral tau algorithm for solving fractional telegraph equation with convergence analysis

In this article, a novel shifted Gegenbauer operational matrix (SGOM) of fractional derivative in the Caputo sense is derived. Based on this operational matrix, an accurate and effective numerical algorithm is proposed.The SGOM of fractional derivative in conjunction with the tau method are used for solving the constant and variable coefficients space–time fractional telegraph equations (FTE) with various types of boundary conditions, namely,Neumann, Dirichlet and Robin conditions. The convergence analysis of the proposed method is established in $\mathcal L^2_{\omega _\alpha}$. Finally, miscellaneous test examples are given and compared with other methods to clarify the accuracy and efficiency of the presented algorithm.

• Efficient method for solving variable-order pantograph models

This paper shows how to solve variable-order pantograph-delay differential equations (VO-PDDEs) and variable-order pantograph Volterra delay integro-differential equations (VO-VDIDEs) using shifted fractional Gegenbauer operational matrices (SFGOMs) of differentiation and integration in conjunction with the spectral collocation method. In these equations, the fractional derivatives of variable order are represented in the Caputo sense. As a result of the proposed method, the considered problems are translated into an easy-to-solve systemof algebraic equations. The proposed technique’s error bound is examined. To demonstrate the utility of the proposed method, numerical test problems are introduced and compared with other numerical methods in theexisting literature.

• # Pramana – Journal of Physics

Volume 96, 2022
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019