Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article The Analytical Analysis of Time-Fractional Fornberg-Whitham Equations(MDPI AG, 2020) Baleanu, Dumitru; Shah, Rasool; Aly, Shaban; Khan, Hassan; Alderremy, A.A.Article Citation - WoS: 28Citation - Scopus: 29The Analytical Analysis of Time-Fractional Fornberg-Whitham Equations(Mdpi, 2020) Khan, Hassan; Shah, Rasool; Aly, Shaban; Baleanu, Dumitru; Alderremy, A. A.This article is dealing with the analytical solution of Fornberg-Whitham equations in fractional view of Caputo operator. The effective method among the analytical techniques, natural transform decomposition method, is implemented to handle the solutions of the proposed problems. The approximate analytical solutions of nonlinear numerical problems are determined to confirm the validity of the suggested technique. The solution of the fractional-order problems are investigated for the suggested mathematical models. The solutions-graphs are then plotted to understand the effectiveness of fractional-order mathematical modeling over integer-order modeling. It is observed that the derived solutions have a closed resemblance with the actual solutions. Moreover, using fractional-order modeling various dynamics can be analyzed which can provide sophisticated information about physical phenomena. The simple and straight-forward procedure of the suggested technique is the preferable point and thus can be used to solve other nonlinear fractional problems.Article Citation - WoS: 40Citation - Scopus: 46Analytical Solution of Fractional-Order Hyperbolic Telegraph Equation, Using Natural Transform Decomposition Method(Mdpi, 2019) Shah, Rasool; Baleanu, Dumitru; Kumam, Poom; Arif, Muhammad; Khan, HassanIn the current paper, fractional-order hyperbolic telegraph equations are considered for analytical solutions, using the decomposition method based on natural transformation. The fractional derivative is defined by the Caputo operator. The present technique is implemented for both fractional- and integer-order equations, showing that the current technique is an accurate analytical instrument for the solution of partial differential equations of fractional-order arising in all branches of applied sciences. For this purpose, several examples related to hyperbolic telegraph models are presented to explain the procedure of the suggested method. It is noted that the procedure of the present technique is simple, straightforward, accurate, and found to be a better mathematical technique to solve non-linear fractional partial differential equations.