Browsing by Author "Talib, Imran"

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Citation - WoS: 4
Citation - Scopus: 4
A Decomposıtıon Algorıthm Coupled Wıth Operatıonal Matrıces Approach Wıth Applıcatıons To Fractıonal Dıfferentıal Equatıons
(Vinca inst Nuclear Sci, 2021) Talib, Imran; Baleanu, Dumitru; Alam, Md Nur; Baleanu, Dumitru; Zaidi, Danish; 56389; Matematik
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: 10
Citation - Scopus: 11
A generalized operational matrix of mixed partial derivative terms with applications to multi-order fractional partial differential equations
(Elsevier, 2022) Talib, Imran; Jarad, Fahd; Jarad, Fahd; Mirza, Muhammad Umar; Nawaz, Asma; Riaz, Muhammad Bilal; 234808; Matematik
In this paper, a computational approach based on the operational matrices in conjunction with orthogonal shifted Legendre polynomials (OSLPs) is designed to solve numerically the multi-order partial differential equations of fractional order consisting of mixed partial derivative terms. Our computational approach has ability to reduce the fractional problems into a system of Sylvester types matrix equations which can be solved by using MATLAB builtin function lyap (.). The solution is approximated as a basis vectors of OSLPs. The efficiency and the numerical stability is examined by taking various test examples. (C) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University.
Citation - WoS: 6
Citation - Scopus: 6
A new integral operational matrix with applications to multi-order fractional differential equations
(Amer inst Mathematical Sciences-aims, 2021) Talib, Imran; Baleanu, Dumitru; Alam, Md Nur; Baleanu, Dumitru; Zaidi, Danish; Marriyam, Ammarah; 56389; Matematik
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.