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A Crank-Nicolson Approximation for the time Fractional Burgers Equation

 and    | Aug 20, 2020

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Podlubny, I., (1998), Fractional Differential Equations, Acasemic Pres, San Diego.PodlubnyI.1998Fractional Differential EquationsAcasemic PresSan DiegoSearch in Google Scholar

Miller, K.S, Ross, B. (1993), An Introduction to The Fractional Calculus and Differential Equations, John Wiley and Sons Ltd.MillerK.SRossB.1993An Introduction to The Fractional Calculus and Differential EquationsJohn Wiley and Sons Ltd.Search in Google Scholar

Smith, G. D. (1986), Numerical Solution of Partial Differential Equations: Finite Difference Methods, Oxford University Press.SmithG. D.1986Numerical Solution of Partial Differential Equations: Finite Difference MethodsOxford University PressSearch in Google Scholar

Youssef, I. K. and El Dewaik, M. H., (2017) Solving Poisson's Equations with fractional order using Haar wavelet, 2,1, 271–284.YoussefI. K.El DewaikM. H.2017Solving Poisson's Equations with fractional order using Haar wavelet2127128410.21042/AMNS.2017.1.00023Search in Google Scholar

Brzeziński, D. W., (2017), Comparison of Fractional Order Derivatives Computational Accuracy - Right Hand vs Left Hand Definition, 2,1, 237–248.BrzezińskiD. W.2017Comparison of Fractional Order Derivatives Computational Accuracy - Right Hand vs Left Hand Definition2123724810.21042/AMNS.2017.1.00020Search in Google Scholar

Brzeziński, D. W., (2018), Review of numerical methods for NumILPT with computational accuracy assessment for fractional calculus, 3, 2, 487–502BrzezińskiD. W.2018Review of numerical methods for NumILPT with computational accuracy assessment for fractional calculus3248750210.2478/AMNS.2018.2.00038Search in Google Scholar

Kilbas, A.A., Srivastava, H.M., Trujillo, J.J., (2006), Theory and Applications of Fractional Differential Equations, Elsevier, AmsterdamKilbasA.A.SrivastavaH.M.TrujilloJ.J.2006Theory and Applications of Fractional Differential EquationsElsevierAmsterdamSearch in Google Scholar

Esen, A., and Tasbozan, O., (2015), Numerical solution of time fractional Burgers equation, Acta Universitatis Sapientiae, Mathematica 7,2, 167–185.EsenA.TasbozanO.2015Numerical solution of time fractional Burgers equationActa Universitatis Sapientiae, Mathematica7216718510.1515/ausm-2015-0011Search in Google Scholar

Esen, A., and Tasbozan O., (2016), Numerical solution of time fractional burgers equation by cubic B-spline finite elements, Mediterranean Journal of Mathematics 13,3, 1325–1337.EsenA.TasbozanO.2016Numerical solution of time fractional burgers equation by cubic B-spline finite elementsMediterranean Journal of Mathematics1331325133710.1007/s00009-015-0555-xSearch in Google Scholar

Qiu, W., Chen H. and Zheng X., (2019), An implicit difference scheme and algorithm implementation for the one-dimensional time-fractional Burgers equations, Mathematics and Computers in Simulation, doi.org/10.1016/j.matcom.2019.05.017.QiuW.ChenH.ZhengX.2019An implicit difference scheme and algorithm implementation for the one-dimensional time-fractional Burgers equationsMathematics and Computers in Simulationdoi.org/10.1016/j.matcom.2019.05.01710.1016/j.matcom.2019.05.017Search in Google Scholar

Mohebbi, A., (2018), Analysis of a Numerical Method for the Solution of Time Fractional Burgers Equation, Bulletin of the Iranian Mathematical Society 44,2 457–480.MohebbiA.2018Analysis of a Numerical Method for the Solution of Time Fractional Burgers EquationBulletin of the Iranian Mathematical Society44245748010.1007/s41980-018-0031-zSearch in Google Scholar

Yaseen, M., and Muhammad A., (2019), An efficient computational technique based on cubic trigonometric B-splines for time fractional Burgers’ equation, International Journal of Computer Mathematics, 1–14, doi.org/10.1080/00207160.2019.1612053.YaseenM.MuhammadA.2019An efficient computational technique based on cubic trigonometric B-splines for time fractional Burgers’ equationInternational Journal of Computer Mathematics114doi.org/10.1080/00207160.2019.161205310.1080/00207160.2019.1612053Search in Google Scholar

Asgari, Z., and Hosseini, S. M., (2018), Efficient numerical schemes for the solution of generalized time fractional Burgers type equations, Numerical Algorithms, 77,3, 763–792.AsgariZ.HosseiniS. M.2018Efficient numerical schemes for the solution of generalized time fractional Burgers type equationsNumerical Algorithms77376379210.1007/s11075-017-0339-4Search in Google Scholar

Alam K., Najeeb, A. A., and Amir M., (2012), Numerical solutions of time-fractional Burgers equations: a comparison between generalized differential transformation technique and homotopy perturbation method, International Journal of Numerical Methods for Heat and Fluid Flow 22,2, 175–193.AlamK.NajeebA. A.AmirM.2012Numerical solutions of time-fractional Burgers equations: a comparison between generalized differential transformation technique and homotopy perturbation methodInternational Journal of Numerical Methods for Heat and Fluid Flow22217519310.1108/09615531211199818Search in Google Scholar

Lombard, B., and Matignon, D., (2017), Numerical modeling of a time-fractional Burgers equation, WAVES, 219–220.LombardB.MatignonD.2017Numerical modeling of a time-fractional Burgers equationWAVES219220Search in Google Scholar

Saad, K. M., and Al-Sharif H.F., (2017), Analytical study for time and time-space fractional Burgers’ equation, Advances in Difference Equations, 2017,300, 1–15.SaadK. M.Al-SharifH.F.2017Analytical study for time and time-space fractional Burgers’ equationAdvances in Difference Equations2017300,11510.1186/s13662-017-1358-0Search in Google Scholar

Murillo, J.Q., Yuste, S.B., (2011), An Explicit Difference Method for solving Fractional Diffusion and Diffusion-Wave Equations in the Caputo Form, J. Comput. Nonlinear Dynam. 6, 021014.MurilloJ.Q.YusteS.B.2011An Explicit Difference Method for solving Fractional Diffusion and Diffusion-Wave Equations in the Caputo FormJ. Comput. Nonlinear Dynam.6021014.10.1115/1.4002687Search in Google Scholar

Oldham, K.B., Spanier, J., (1974), The Fractional Calculus, Academic, New YorkOldhamK.B.SpanierJ.1974The Fractional CalculusAcademicNew YorkSearch in Google Scholar

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