
AIMS Mathematics, 2020, 5(1): 114. doi: 10.3934/math.2020001.
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A new computational for approximate analytical solutions of nonlinear timefractional wavelike equations with variable coefficients
Laboratory of Fundamental and Numerical Mathematics, Department of Mathematics, Faculty of Sciences, Ferhat Abbas University of Sétif 1, Sétif 19000, Algeria
Received: , Accepted: , Published:
Special Issues: Recent Advances in Fractional Calculus with Real World Applications
Keywords: nonlinear timefractional wavelike equations; Caputo fractional derivative; fractional residual power series method
Citation: Ali Khalouta, Abdelouahab Kadem. A new computational for approximate analytical solutions of nonlinear timefractional wavelike equations with variable coefficients. AIMS Mathematics, 2020, 5(1): 114. doi: 10.3934/math.2020001
References:
 1. O. Abu Arqub, Series solution of fuzzy differential equations under strongly generalized differentiability, J. Adv. Res. Appl. Math., 5 (2013), 3152.
 2. O. Acan, M. M. Al Qurashi and D. Baleanu, Reduced differential transform method for solving time and space local fractional partial differential equations, J. Nonlinear Sci. Appl., 10 (2017), 52305238.
 3. M. Dehghan, J. Manafian and A. Saadatmandi, Solving nonlinear fractional partial differential equations using the homotopy analysis method, Numer. Meth. Part. D. E., 26 (2009), 448479.
 4. A. ElAjou, O. Abu Arqub, Z. Al Zhour, et al. New results on fractional power series: theories and applications, Entropy, 15 (2013), 53055323.
 5. A. ElAjou, O. AbuArquba and Sh. Momanib, Approximate analytical solution of the nonlinear fractional KdVBurgers equation: A new iterative algorithm, J. Comput. Phys., 293 (2015), 8195.
 6. A. Elsaid, The variational iteration method for solving Riesz fractional partial differential equations, Comput. Math. Appl., 60 (2010), 19401947.
 7. A. A. Freihet and M. Zuriqat, Analytical Solution of Fractional BurgersHuxley Equations via Residual Power Series Method, Lobachevskii Journal of Mathematics, 40 (2019), 174182.
 8. P. K. Gupta and M. Singh, Homotopy perturbation method for fractional FornbergWhitham equation, Comput. Math. Appl., 61 (2011), 250254.
 9. K. Hosseini, A. Bekir, M. Kaplan, et al. On On a new technique for solving the nonlinear conformable timefractional differential equations, Opt. Quant. Electron., 49 (2017), 343.
 10. M. Kaplan, A. Bekir, A. Akbulut, et al. The modified simple equation method for nonlinear fractional differential equations, Rom. J. Phys., 60 (2015), 13741383.
 11. M. Kaplan and A. Bekir, Construction of exact solutions to the spacetime fractional differential equations via new approach, Optik, 132 (2017), 18.
 12. A. Khalouta and A. Kadem, Comparison of New Iterative Method and Natural Homotopy Perturbation Method for Solving Nonlinear TimeFractional WaveLike Equations with Variable Coefficients, Nonlinear Dyn. Syst. Theory, 19 (2019), 160169.
 13. A. Khalouta and A. Kadem, Fractional natural decomposition method for solving a certain class of nonlinear timefractional wavelike equations with variable coefficients, Acta Universitatis Sapientiae: Mathematica, 11 (2019), 99116.
 14. A. Khalouta and A. Kadem, A New Technique for Finding Exact Solutions of Nonlinear TimeFractional WaveLike Equations with Variable Coefficients, Proc. Inst. Math. Mech. Natl. Acad.Sci. Azerb., 2019.
 15. A. Khalouta and A. Kadem, A New iterative natural transform method for solving nonlinear Caputo timefractional partial differential equations, Appear in: Jordan J. Math. Stat., 2019.
 16. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Application of Fractional Differential equations, Elsevier, Amsterdam, 2006.
 17. A. Kumar, S. Kumar and M. Singh, Residual power series method for fractional SharmaTassoOlever equation, Commun. Numer. Anal., 2016 (2016), 110.
 18. K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Willey and Sons, New York, 1993.
 19. Z. Pinar, On the explicit solutions of fractional BagleyTorvik equation arises in engineering, An International Journal of Optimization and Control: Theories & Applications (IJOCTA), 9 (2019), 5258.
 20. I. Podlubny, Fractional Differential Equations, Academic Press, New York, 1999.
 21. F. Tchier, M. Inc, Z. S. Korpinar, et al. Solutions of the time fractional reactiondiffusion equations with residual power series method, Adv. Mech. Eng., 8 (2016), 110.
 22. H. Thabet and S. Kendre, New modification of Adomian decomposition method for solving a system of nonlinear fractional partial differential equations, Int. J. Adv. Appl. Math. and Mech., 6 (2019), 113.
 23. S. Uçar, E. Uçar, N. Özdemira, et al. Mathematical analysis and numerical simulation for a smoking model with AtanganaBaleanu derivative, Chaos Solitons Fractals, 118 (2019), 300306.
 24. M. Yavuz, Novel solution methods for initial boundary value problems of fractional order with conformable differentiation, An International Journal of Optimization and Control: Theories & Applications (IJOCTA), 8 (2017), 17.
 25. M. Yavuz and N. Özdemira, Comparing the new fractional derivative operators involving exponential and MittagLeffler kernel, Discrete Contin. Dyn. Syst. Ser. S, 13 (2020), 9951006.
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