WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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Article Citation - WoS: 10Citation - Scopus: 8Derivation of Operational Matrix of Rabotnov Fractional-Exponential Kernel and Its Application To Fractional Lienard Equation(Elsevier, 2020) Gomez-Aguilar, J. F.; Lavin-Delgado, J. E.; Baleanu, D.; Kumar, SachinOur motive in this contribution is to find out the operational matrix of fractional derivative having non singular kernel namely Rabotnov fractional-exponential (RFE) kernel which is recently introduced and seeking numerical solution of non-linear Lienard equation which have Rabotnov fractional-exponential kernel fractional derivative. First we derive an approximation formula of the fractional order derivative of polynomial function z(k) in term of RFE kernel. Using this formula and some properties of shifted Legendre polynomials, we find out the operational matrix of fractional order differentiation. In the author of knowledge this operational matrix of RFE kernel fractional derivative is derived first time. We solve a new class of fractional partial differential equation (FPDEs) by implementation of this newly derived operational matrix. We show that our newly derived operational matrix is valid by taking an fractional derivative of a polynomial. Also, we study a new model of Lienard equation with RFE kernel fractional derivative and we can easily predict the feasibility of our numerical method to this new model. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University.Article Citation - WoS: 69Citation - Scopus: 91Fractional Lienard Type Model of a Pipeline Within the Fractional Derivative Without Singular Kernel(Springeropen, 2016) Torres, L.; Yepez-Martinez, H.; Baleanu, D.; Reyes, J. M.; Sosa, I. O.; Gomez-Aguilar, J. F.This paper presents the procedure to obtain analytical solutions of Li,nard type model of a fluid transmission line represented by the Caputo-Fabrizio fractional operator. For such a model, we derive a new approximated analytical solution by using the Laplace homotopy analysis method. Both the efficiency and the accuracy of the method are verified by comparing the obtained solutions with the exact analytical solution. Good agreement between them is confirmed.