WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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Article Citation - WoS: 37Citation - Scopus: 40The Analytical Investigation of Time-Fractional Multi-Dimensional Navier-Stokes Equation(Elsevier, 2020) Khan, Hassan; Baleanu, Dumitru; Kumam, Poom; Arif, Muhammad; Shah, RasoolIn the present research article, we implemented two well-known analytical techniques to solve fractional-order multi-dimensional Navier-Stokes equation. The proposed methods are the modification of Adomian decomposition method and variational iteration method by using natural transformation. Furthermore, some illustrative examples are presented to confirm the validity of the suggested methods. The solutions graphs and tables are constructed for both fractional and integer-order problems. It is investigated that the suggested techniques have the identical solutions of the problems. The solution comparison via graphs and tables have also supported the greater accuracy and higher rate of convergence of the present methods. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University.Article Citation - WoS: 31Citation - Scopus: 39Fractional View Analysis of Third Order Kortewege-De Vries Equations, Using a New Analytical Technique(Frontiers Media Sa, 2020) Farooq, Umar; Khan, Hassan; Baleanu, Dumitru; Kumam, Poom; Arif, Muhammad; Shah, RasoolIn the present article, fractional view of third order Kortewege-De Vries equations is presented by a sophisticated analytical technique called Mohand decomposition method. The Caputo fractional derivative operator is used to express fractional derivatives, containing in the targeted problems. Some numerical examples are presented to show the effectiveness of the method for both fractional and integer order problems. From the table, it is investigated that the proposed method has the same rate of convergence as compare to homotopy perturbation transform method. The solution graphs have confirmed the best agreement with the exact solutions of the problems and also revealed that if the sequence of fractional-orders is approaches to integer order, then the fractional order solutions of the problems are converge to an integer order solution. Moreover, the proposed method is straight forward and easy to implement and therefore can be used for other non-linear fractional-order partial differential equations.Article Citation - WoS: 34Citation - Scopus: 41Analytical Solutions of (2+time Fractional Order) Dimensional Physical Models, Using Modified Decomposition Method(Mdpi, 2020) Farooq, Umar; Shah, Rasool; Baleanu, Dumitru; Kumam, Poom; Arif, Muhammad; Khan, HassanIn this article, a new analytical technique based on an innovative transformation is used to solve (2+time fractional-order) dimensional physical models. The proposed method is the hybrid methodology of Shehu transformation along with Adomian decomposition method. The series form solution is obtained by using the suggested method which provides the desired rate of convergence. Some numerical examples are solved by using the proposed method. The solutions of the targeted problems are represented by graphs which have confirmed closed contact between the exact and obtained solutions of the problems. Based on the novelty and straightforward implementation of the method, it is considered to be one of the best analytical techniques to solve linear and non-linear fractional partial differential equations.Article Citation - WoS: 37Citation - Scopus: 38A New Analytical Technique To Solve System of Fractional-Order Partial Differential Equations(Ieee-inst Electrical Electronics Engineers inc, 2019) Khan, Hassan; Farooq, Umar; Baleanu, Dumitru; Kumam, Poom; Arif, Muhammad; Shah, RasoolIn this research article, a new analytical technique is implemented to solve system of fractional-order partial differential equations. The fractional derivatives are carried out with the help of Caputo fractional derivative operator. The direct implementation of Mohand and its inverse transformation provide sufficient easy less and reliability of the proposed method. Decomposition method along with Mohand transformation is proceeded to attain the analytical solution of the targeted problems. The applicability of the suggested method is analyzed through illustrative examples. The solutions graph has the best contact with the graphs of exact solutions in paper. Moreover, the convergence of the present technique is sufficiently fast, so that it can be considered the best technique to solve system of nonlinear fractional-order partial differential equations.