TY - JOUR AU - Diethelm, K. AU - Ford, N. J. AU - Freed, D. PY - 2009 DA - 2009// TI - A predictor-corrector approach for the numerical solution of fractional differential equation JO - Nonlinear Dyn VL - 29 ID - Diethelm2009 ER - TY - BOOK AU - Baleanu, D. AU - Diethelm, K. AU - Scalas, E. AU - Trujillo, J. PY - 2012 DA - 2012// TI - Fractional Calculus Models and Numerical Methods PB - World Scientific CY - Boston ID - Baleanu2012 ER - TY - JOUR AU - Saha Ray, S. AU - Bera, R. K. PY - 2005 DA - 2005// TI - An approximate solution of a nonlinear fractional differential equation by Adomian decomposition method JO - Appl. Math. Comput VL - 167 UR - https://doi.org/10.1016/j.amc.2004.07.020 DO - 10.1016/j.amc.2004.07.020 ID - Saha Ray2005 ER - TY - JOUR AU - Hu, Y. AU - Luo, Y. AU - Lu, Z. PY - 2008 DA - 2008// TI - Analytical solution of the linear fractional differential equation by Adomian decomposition method JO - J. Comput. Appl. Math VL - 215 UR - https://doi.org/10.1016/j.cam.2007.04.005 DO - 10.1016/j.cam.2007.04.005 ID - Hu2008 ER - TY - JOUR AU - Duan, J. -. S. AU - Rach, R. AU - Baleanu, D. AU - Wazwaz, A. -. M. PY - 2012 DA - 2012// TI - A review of the Adomian decomposition method and its applications to fractional differential equations JO - Commun. Fract. Calc VL - 3 ID - Duan2012 ER - TY - JOUR AU - Hashim, I. AU - Abdulaziz, O. AU - Momani, S. PY - 2009 DA - 2009// TI - Homotopy analysis method for fractional IVPs JO - Commun. Nonlinear Sci. Numer. Simul VL - 14 UR - https://doi.org/10.1016/j.cnsns.2007.09.014 DO - 10.1016/j.cnsns.2007.09.014 ID - Hashim2009 ER - TY - JOUR AU - Odibat, Z. AU - Momani, S. AU - Xu, H. PY - 2010 DA - 2010// TI - A reliable algorithm of homotopy analysis method for solving nonlinear fractional differential equations JO - Appl. Math. Model VL - 34 UR - https://doi.org/10.1016/j.apm.2009.06.025 DO - 10.1016/j.apm.2009.06.025 ID - Odibat2010 ER - TY - JOUR AU - Elsaid, A. PY - 2011 DA - 2011// TI - Homotopy analysis method for solving a class of fractional partial differential equations JO - Commun. Nonlinear Sci. Numer. Simul VL - 16 UR - https://doi.org/10.1016/j.cnsns.2010.12.040 DO - 10.1016/j.cnsns.2010.12.040 ID - Elsaid2011 ER - TY - JOUR AU - Abdulaziz, O. AU - Hashim, I. AU - Momani, S. PY - 2008 DA - 2008// TI - Application of homotopy-perturbation method to fractional IVPs JO - J. Comput. Appl. Math VL - 216 UR - https://doi.org/10.1016/j.cam.2007.06.010 DO - 10.1016/j.cam.2007.06.010 ID - Abdulaziz2008 ER - TY - JOUR AU - Abdulaziz, O. AU - Hashim, I. AU - Momani, S. PY - 2008 DA - 2008// TI - Solving systems of fractional differential equations by homotopy-perturbation method JO - Phys. Lett. A VL - 372 UR - https://doi.org/10.1016/j.physleta.2007.07.059 DO - 10.1016/j.physleta.2007.07.059 ID - Abdulaziz2008 ER - TY - JOUR AU - Das, S. PY - 2009 DA - 2009// TI - Analytical solution of a fractional diffusion equation by variational iteration method JO - Comput. Math. Appl VL - 57 UR - https://doi.org/10.1016/j.camwa.2008.09.045 DO - 10.1016/j.camwa.2008.09.045 ID - Das2009 ER - TY - JOUR AU - Guo, S. AU - Mei, L. PY - 2011 DA - 2011// TI - The fractional variational iteration method using He’s polynomials JO - Phys. Lett. A VL - 375 UR - https://doi.org/10.1016/j.physleta.2010.11.047 DO - 10.1016/j.physleta.2010.11.047 ID - Guo2011 ER - TY - JOUR AU - Wu, G. -. c. PY - 2011 DA - 2011// TI - A fractional variational iteration method for solving fractional nonlinear differential equations JO - Comput. Math. Appl VL - 61 UR - https://doi.org/10.1016/j.camwa.2010.09.010 DO - 10.1016/j.camwa.2010.09.010 ID - Wu2011 ER - TY - JOUR AU - Wu, G. C. AU - Baleanu, D. PY - 2012 DA - 2012// TI - Variational iteration method for the Burgers flow with fractional derivatives-New Lagrange multipliers JO - Appl. Math. Model VL - 37 UR - https://doi.org/10.1016/j.apm.2012.12.018 DO - 10.1016/j.apm.2012.12.018 ID - Wu2012 ER - TY - CHAP AU - Wu, G. C. AU - Baleanu, D. PY - 2013 DA - 2013// TI - Variational iteration method for fractional calculus - a universal approach by Laplace transform BT - Adv. Differ. Equ ID - Wu2013 ER - TY - JOUR AU - Arikoglum, A. AU - Ozkol, I. PY - 2007 DA - 2007// TI - Solution of fractional differential equations by using differential transform method JO - Chaos Solitons Fractals VL - 34 UR - https://doi.org/10.1016/j.chaos.2006.09.004 DO - 10.1016/j.chaos.2006.09.004 ID - Arikoglum2007 ER - TY - JOUR AU - Odibat, Z. AU - Shawagfeh, N. PY - 2007 DA - 2007// TI - Generalized Talyor’s formula JO - Appl. Math. Comput VL - 186 UR - https://doi.org/10.1016/j.amc.2006.07.102 DO - 10.1016/j.amc.2006.07.102 ID - Odibat2007 ER - TY - JOUR AU - Odibat, Z. AU - Momani, S. AU - Erturk, V. S. PY - 2008 DA - 2008// TI - Generalized differential transform method: application to differential equations of fractional order JO - Appl. Math. Comput VL - 197 UR - https://doi.org/10.1016/j.amc.2007.07.068 DO - 10.1016/j.amc.2007.07.068 ID - Odibat2008 ER - TY - JOUR AU - Caputo, M. PY - 1967 DA - 1967// TI - Linear models of dissipation whose Q is almost frequency independent. Part II JO - Geophys. J. R. Astron. Soc VL - 13 UR - https://doi.org/10.1111/j.1365-246X.1967.tb02303.x DO - 10.1111/j.1365-246X.1967.tb02303.x ID - Caputo1967 ER - TY - JOUR AU - Jang, M. J. AU - Chen, C. L. AU - Liu, Y. C. PY - 2000 DA - 2000// TI - On solving the initial-value problems using the differential transformation method JO - Appl. Math. Comput VL - 115 UR - https://doi.org/10.1016/S0096-3003(99)00137-X DO - 10.1016/S0096-3003(99)00137-X ID - Jang2000 ER - TY - JOUR AU - Jang, M. J. AU - Chen, C. L. AU - Liu, Y. C. PY - 2001 DA - 2001// TI - Two-dimensional differential transform for partial differential equations JO - Appl. Math. Comput VL - 121 UR - https://doi.org/10.1016/S0096-3003(99)00293-3 DO - 10.1016/S0096-3003(99)00293-3 ID - Jang2001 ER - TY - JOUR AU - Ravi Kanth, A. S. V. AU - Aruna, K. PY - 2009 DA - 2009// TI - Differential transform method for solving the linear and nonlinear Klein-Gordon equation JO - Comput. Phys. Commun VL - 180 UR - https://doi.org/10.1016/j.cpc.2008.11.012 DO - 10.1016/j.cpc.2008.11.012 ID - Ravi Kanth2009 ER - TY - JOUR AU - Jang, B. PY - 2009 DA - 2009// TI - Comments on ‘Solving a class of two-dimensional linear and nonlinear Volterra integral equations by the differential transform method’ JO - J. Comput. Appl. Math VL - 233 UR - https://doi.org/10.1016/j.cam.2009.07.012 DO - 10.1016/j.cam.2009.07.012 ID - Jang2009 ER - TY - JOUR AU - Jang, B. PY - 2010 DA - 2010// TI - Solving linear and nonlinear initial value problems by the projected differential transform method JO - Comput. Phys. Commun VL - 181 UR - https://doi.org/10.1016/j.cpc.2009.12.020 DO - 10.1016/j.cpc.2009.12.020 ID - Jang2010 ER - TY - JOUR AU - Odibat, Z. AU - Bertelle, C. AU - Aziz-Alaoui, M. A. AU - Duchamp, G. H. E. PY - 2010 DA - 2010// TI - A multi-step differential transform method and application to non-chaotic or chaotic systems JO - Comput. Math. Appl VL - 59 UR - https://doi.org/10.1016/j.camwa.2009.11.005 DO - 10.1016/j.camwa.2009.11.005 ID - Odibat2010 ER - TY - JOUR AU - Alomari, A. K. PY - 2011 DA - 2011// TI - A new analytic solution for fractional chaotic dynamical systems using the differential transform method JO - Comput. Math. Appl VL - 61 UR - https://doi.org/10.1016/j.camwa.2011.02.043 DO - 10.1016/j.camwa.2011.02.043 ID - Alomari2011 ER - TY - JOUR AU - Gökdoğan, A. AU - Yildirim, A. AU - Merdan, M. PY - 2011 DA - 2011// TI - Solving a fractional order model of HIV infection of CD4+ T cells JO - Math. Comput. Model VL - 54 UR - https://doi.org/10.1016/j.mcm.2011.05.022 DO - 10.1016/j.mcm.2011.05.022 ID - Gökdoğan2011 ER - TY - JOUR AU - Elsaid, A. PY - 2012 DA - 2012// TI - Fractional differential transform method combined with the Adomian polynomials JO - Appl. Math. Comput VL - 218 UR - https://doi.org/10.1016/j.amc.2011.12.066 DO - 10.1016/j.amc.2011.12.066 ID - Elsaid2012 ER -