@Article{Benson2000, author=" D. A. Benson, S. W. Wheatcraft, M. M. Meerschaert", title="Application of a fractional advection-dispersion equation", journal="Water Resour. Res.", year="2000", pages=" 1403–1412. ", volume="36" } @Article{Chen2010, author=" W. Chen, L.-J. Ye, H.-G. Sun", title="Fractional diffusion equations by the Kansa method", journal=" Comput. Math. Appl.", year="2010", pages="1614–1620. ", volume="59" } @Article{Clarkson1989, author="P. A. Clarkson", title=" New similarity solutions for the modified Boussinesq equation", journal=" J. Phys. A", year="1989", pages="2355–2367. ", volume="22" } @Article{Elwakil2002, author=" S. A. Elwakil, S. K. El-labany, M. A. Zahran, R. Sabry", title=" Modified extended tanh-function method for solving nonlinear partial differential equations", journal=" Phys. Lett. A", year="2002", pages=" 179–188. ", volume="299" } @Article{Fan2000, author=" E.-G. Fan", title="Extended tanh-function method and its applications to nonlinear equations", journal=" Phys. Lett. A", year="2000", pages="212–218. ", volume="277" } @Article{Gorguis2006, author="A. Gorguis", title="A comparison between Cole-Hopf transformation and the decomposition method for solving Burgers’ equations", journal=" Appl. Math. Comput.", year="2006", pages="126–136. ", volume="173" } @Article{Guo2010, author=" S.-M. Guo, Y.-B. Zhou", title="The extended (\(\frac{G'}{G}\) )-expansion method and its applications to the Whitham-Broer-Kaup-like equations and coupled Hirota-Satsuma KdV equations", journal="Appl. Math. Comput.", year="2010", pages=" 3214–3221. ", volume="215" } @Article{He2006, author=" J.-H. He, X.-H. Wu", title="Exp-function method for nonlinear wave equations", journal=" Chaos Solitons Fractals", year="2006", pages=" 700–708. ", volume="30" } @Article{Islam2008, author="S. U. Islam, A. J. Khattakand, I. A. Tirmizi", title=" A meshfree method for numerical solution of KdV equation", journal="Eng. Anal. Bound. Elem.", year="2008", pages="849–855.", volume="32" } @Article{Liu2007, author=" F. Liu, P. Zhuang, V. Anh, I. Turner, K. Burrage", title=" Stability and convergence of the difference methods for the space-time fractional advection-diffusion equation", journal="Appl. Math. Comput.", year="2007", pages=" 12–20. ", volume="191" } @Article{Mainardi2000, author=" F. Mainardi, M. Raberto, R. Gorenflo, E. Scalas", title=" Fractional calculus and continuous-time finance, II, the waiting-time distribution", journal="Phys. A", year="2000", pages="468–481. ", volume="287" } @Article{Meerschaert2004, author="M. M. Meerschaert, C. Tadjeran", title="Finite difference approximations for fractional advection-dispersion flow equations", journal="J. Comput. Appl. Math.", year="2004", pages="65–77. ", volume="172" } @Book{Miller1993, author=" K. S. Miller, B. Ross", title="An introduction to the fractional calculus and fractional differential equations", year="1993", publisher="A Wiley-Interscience Publication, John Wiley & Sons, Inc.", address=" New York" } @Article{Odibat2007, author=" Z. M. Odibat, N. T. Shawagfeh", title=" Generalized Taylor’s formula", journal=" Appl. Math. Comput.", year="2007", pages=" 286–293. ", volume="186" } @Book{Oldham2006, author="K. B. Oldham, J. Spanier", title=" The fractional calculus", year="2006", publisher="Theory and applications of differentiation and integration to arbitrary order, With an annotated chronological bibliography by Bertram Ross, Mathematics in Science and Engineering, Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers]", address="New York-London" } @Article{Parkes1996, author=" E. J. Parkes, B. R. Duffy", title="An automated tanh-function method for finding solitary wave solutions to non-linear evolution equations", journal="Comput. Phys. Commun.", year="1996", pages="288–300. ", volume="98" } @Book{Podlubny1999, author="I. Podlubny", title="Fractional differential equations", year="1999", publisher=" An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications, Mathematics in Science and Engineering, Academic Press, Inc.", address=" San Diego, CA" } @Article{Scalas2000, author="E. Scalas, R. Gorenflo, F. Mainardi", title="Fractional calculus and continuous-time finance", journal="Phys. A", year="2000", pages="376–384. ", volume="284" } @Article{Sousa2009, author="E. Sousa", title="Finite difference approximations for a fractional advection diffusion problem", journal="J. Comput. Phys.", year="2009", pages="4038–4054. ", volume="228" } @Article{Su2010, author="L.-J. Su, W.-Q. Wang, Q.-Y. Xu", title="Finite difference methods for fractional dispersion equations", journal="Appl. Math. Comput.", year="2010", pages="3329–3334. ", volume="216" } @Article{Su2009, author="L.-J. Su, W.-Q. Wang, Z.-X. Yang", title=" Finite difference approximations for the fractional advection-diffusion equation", journal=" Phys. Lett. A", year="2009", pages="4405–4408. ", volume="373" } @Article{Wang2008, author=" M.-L. Wang, X.-Z. Li, J.-L. Zhang", title="The (\(\frac{G'}{G}\) )-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics", journal=" Phys. Lett. A", year="2008", pages=" 417–423. ", volume="372" } @Article{Wazwaz2005, author="A. M. Wazwaz", title=" The tanh method: solitons and periodic solutions for the Dodd-Bullough-Mikhailov and the Tzitzeica-Dodd- Bullough equations", journal=" Chaos Solitons Fractals", year="2005", pages="55–63. ", volume="25" } @Book{Yokus2011, author=" A. Yokus", title="Solutions of some nonlinear partial differential equations and comparison of their solutions", year="2011", publisher=" Ph.D. Thesis, Fırat University, Elazig", address="Turkey" } @Article{Yuste2006, author=" S. B. Yuste", title="Weighted average finite difference methods for fractional diffusion equations", journal="J. Comput. Phys. ", year="2006", pages=" 264–274.", volume="216" } @Article{Zaslavsky2002, author=" G. M. Zaslavsky", title="Chaos, fractional kinetics, and anomalous transport", journal=" Phys. Rep.", year="2002", pages=" 461–580. ", volume="371" } @Article{Zheng2003, author="X.-D. Zheng, Y. Chen, H.-Q. Zhang", title="Generalized extended tanh-function method and its application to (1+1)-dimensional dispersive long wave equation", journal="Phys. Lett. A", year="2003", pages=" 145–157.", volume="311" } @Article{Zhuang2008, author=" P. Zhuang, F. Liu, V. Anh, I. Turner", title="New solution and analytical techniques of the implicit numerical method for the anomalous subdiffusion equation", journal=" SIAM J. Numer. Anal.", year="2008", pages=" 1079–1095.", volume="46" }