Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Citation - WoS: 7Citation - Scopus: 7A 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, ImranIn 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.Article YFICITIOUS TIME INTEGRATION METHOD FOR SOLVING THE TIME FRACTIONAL GAS DYNAMICS EQUATION(2019) Partohaghighi, Mohammad; İnç, Mustafa; Baleanu, Dumitru; Moshokoa, Seithuti PhilemonIn this work a poweful approach is presented to solve the time-fractional gas dynamics equation. In fact, we use a fictitious time variable y to convert the dependent variable w(x, t) into a new one with one more dimension. Then by taking a initial guess and implementing the group preserving scheme we solve the problem. Finally four examples are solved to illustrate the power of the offered method.Article Citation - WoS: 17Citation - Scopus: 17Yficitious Time Integration Method for Solving the Time Fractional Gas Dynamics Equation(Vinca inst Nuclear Sci, 2019) Inc, Mustafa; Baleanu, Dumitru; Moshokoa, Seithuti Philemon; Partohaghighi, MohammadIn this work a poweful approach is presented to solve the time-fractional gas dynamics equation. In fact, we use a fictitious time variable y to convert the dependent variable w(x, t) into a new one with one more dimension. Then by taking a initial guess and implementing the group preserving scheme we solve the problem. Finally four examples are solved to illustrate the power of the offered method.