Browsing by Author "Hajira"

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Citation Count: Khan, Hassan;...et.al. "An approximate analytical solution of the Navier–Stokes equations within Caputo operator and Elzaki transform decomposition method", Advances in Difference Equations, Vol.2020, No.1.
An approximate analytical solution of the Navier–Stokes equations within Caputo operator and Elzaki transform decomposition method
(2020) Hajira; Khan, Hassan; Khan, Adnan; Kumam, Poom; Baleanu, Dumitru; Arif, Muhammad; 56389
In this article, a hybrid technique of Elzaki transformation and decomposition method is used to solve the Navier–Stokes equations with a Caputo fractional derivative. The numerical simulations and examples are presented to show the validity of the suggested method. The solutions are determined for the problems of both fractional and integer orders by a simple and straightforward procedure. The obtained results are shown and explained through graphs and tables. It is observed that the derived results are very close to the actual solutions of the problems. The fractional solutions are of special interest and have a strong relation with the solution at the integer order of the problems. The numerical examples in this paper are nonlinear and thus handle its solutions in a sophisticated manner. It is believed that this work will make it easy to study the nonlinear dynamics, arising in different areas of research and innovation. Therefore, the current method can be extended for the solution of other higher-order nonlinear problems.
Citation Count: Hajira...et al (2020). "Exact solutions of the Laplace fractional boundary value problems via natural decomposition method", Open Physics, Vol. 18, No. 1, pp. 1178-1187.
Exact solutions of the Laplace fractional boundary value problems via natural decomposition method
(2020) Hajira; Khan, Hassan; Chu, Yu-Ming; Shah, Rasool; Baleanu, Dumitru; Arif, Muhammad; 56389
In this article, exact solutions of some Laplace-type fractional boundary value problems (FBVPs) are investigated via natural decomposition method. The fractional derivatives are described within Caputo operator. The natural decomposition technique is applied for the first time to boundary value problems (BVPs) and found to be an excellent tool to solve the suggested problems. The graphical representation of the exact and derived results is presented to show the reliability of the suggested technique. The present study is mainly concerned with the approximate analytical solutions of some FBVPs. Moreover, the solution graphs have shown that the actual and approximate solutions are very closed to each other. The comparison of the proposed and variational iteration methods is done for integer-order problems. The comparison, support strong relationship between the results of the suggested techniques. The overall analysis and the results obtained have confirmed the effectiveness and the simple procedure of natural decomposition technique for obtaining the solution of BVPs. © 2020 Hajira et al., published by De Gruyter 2020.