Browsing by Author "Alam, Md Nur"

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Citation - WoS: 24
Citation - Scopus: 29
Closed-Form Solutions To the Solitary Wave Equation in an Unmagnatized Dusty Plasma
(Elsevier, 2020) Seadawy, Aly R.; Baleanu, Dumitru; Alam, Md Nur; 56389
The research of unmagnetized dusty plasmas is extremely amiable as long as theoretical aspects and their applicability. They are an outstanding mechanism for generating exact solitary waves and solitons. The present article examines the KdV-Burgers type equation in an unmagnetized dusty plasma and the Kadomtsev-Petviashvili dynamical equation in unmagnetized dust plasma. We present the modified (G'/G)-expansion process to secure few exact solitary wave answers. The acquired outcomes confirm that the studied method is an outspoken and useful analytical device for NLEEs in mathematical physics. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University.
Citation - WoS: 21
Citation - Scopus: 28
Closed-Form Wave Structures of the Space-Time Fractional Hirota-Satsuma Coupled Kdv Equation With Nonlinear Physical Phenomena
(de Gruyter Poland Sp Z O O, 2020) Seadawy, Aly R.; Baleanu, Dumitru; Alam, Md Nur; 56389
The present paper applies the variation of (G'/G)-expansion method on the space-time fractional Hirota-Satsuma coupled KdV equation with applications in physics. We employ the new approach to receive some closed form wave solutions for any nonlinear fractional ordinary differential equations. First, the fractional derivatives in this research are manifested in terms of Riemann-Liouville derivative. A complex fractional transformation is applied to transform the fractional-order ordinary and partial differential equation into the integer order ordinary differential equation. The reduced equations are then solved by the method. Some novel and more comprehensive solutions of these equations are successfully constructed. Besides, the intended approach is simplistic, conventional, and able to significantly reduce the size of computational work associated with other existing methods.
Citation - WoS: 7
Citation - Scopus: 6
A Decomposition Algorithm Coupled With Operational Matrices Approach With Applications To Fractional Differential Equations
(Vinca inst Nuclear Sci, 2021) Alam, Md Nur; Baleanu, Dumitru; Zaidi, Danish; Talib, Imran; 56389
In this article, we solve numerically the linear and non-linear fractional initial value problems of multiple orders by developing a numerical method that is based on the decomposition algorithm coupled with the operational matrices approach. By means of this, the fractional initial value problems of multiple orders are decomposed into a system of fractional initial value problems which are then solved by using the operational matrices approach. The efficiency and advantage of the developed numerical method are highlighted by comparing the results obtained otherwise in the literature. The construction of the new derivative operational matrix of fractional legendre function vectors in the Caputo sense is also a part of this research. As applications, we solve several fractional initial value problems of multiple orders. The numerical results are displayed in tables and plots.
Citation - WoS: 7
Citation - Scopus: 7
A New Integral Operational Matrix With Applications To Multi-Order Fractional Differential Equations
(Amer inst Mathematical Sciences-aims, 2021) Alam, Md Nur; Baleanu, Dumitru; Zaidi, Danish; Marriyam, Ammarah; Talib, Imran; 56389
In this article, we propose a numerical method that is completely based on the operational matrices of fractional integral and derivative operators of fractional Legendre function vectors (FLFVs). The proposed method is independent of the choice of the suitable collocation points and expansion of the residual function as a series of orthogonal polynomials as required for Spectral collocation and Spectral tau methods. Consequently, the high efficient numerical results are obtained as compared to the other methods in the literature. The other novel aspect of our article is the development of the new integral and derivative operational matrices in Riemann-Liouville and Caputo senses respectively. The proposed method is computer-oriented and has the ability to reduce the fractional differential equations (FDEs) into a system of Sylvester types matrix equations that can be solved using MATLAB builtin function lyap(.). As an application of the proposed method, we solve multi-order FDEs with initial conditions. The numerical results obtained otherwise in the literature are also improved in our work.