TY - JOUR TI - Fractional calculus in the transient analysis of viscoelastically damped structures AU - R. L. Bagley AU - P. J. Torvik JO - AIAA J. PY - 1985 DA - 1985// VL - 23 ID - Bagley1985 ER - TY - JOUR TI - An algorithm for the numerical solution of differential equations of fractional order AU - K. Diethelm JO - Electron. Trans. Numer. Anal. PY - 1997 DA - 1997// VL - 5 ID - Diethelm1997 ER - TY - JOUR TI - Numerical solution of the Bagley-Torvik equation AU - K. Diethelm AU - N. J. Ford JO - BIT PY - 2002 DA - 2002// VL - 42 ID - Diethelm2002 ER - TY - JOUR TI - A predictor-Corrector approach for the numerical solution of fractional differential equations AU - K. Diethelm AU - N. J. Ford AU - A. D. Freed JO - Nonlinear Dynam. PY - 2002 DA - 2002// VL - 29 ID - Diethelm2002 ER - TY - JOUR TI - Numerical solution of fractional order differential equations by extrapolation AU - K. Diethelm AU - G. Walz JO - Numer. Algorithms PY - 1997 DA - 1997// VL - 16 ID - Diethelm1997 ER - TY - JOUR TI - An analog simulation of non-integer order transfer functions for analysis of electrode processes AU - M. Ichise AU - Y. Nagayanagi AU - T. Kojima JO - J. Electroanal. Chem. PY - 1971 DA - 1971// VL - 33 ID - Ichise1971 ER - TY - JOUR TI - A modified numerical scheme and convergence analysis for fractional model of Lienard’s equation AU - D. Kumar AU - R. P. Agarwal AU - J. Singh JO - J. Comput. Appl. Math. PY - 2017 DA - 2017// VL - ID - Kumar2017 ER - TY - JOUR TI - A fractional model of convective radial fins with temperature-dependent thermal conductivity AU - D. Kumar AU - J. Singh AU - D. Baleanu JO - Romanian Reports in Physics PY - 2017 DA - 2017// VL - 2017 ID - Kumar2017 ER - TY - JOUR TI - Modified Kawahara equation within a fractional derivative with non-singular kernel AU - D Kumar AU - J. Singh AU - D. Baleanu JO - Therm. Sci. PY - 2017 DA - 2017// VL - 2017 ID - Kumar2017 ER - TY - JOUR TI - Numerical solution of the space fractional Fokker-Planck equation AU - F. Liu AU - V. Anh AU - I. Turner JO - J. Comput. Appl. Math. PY - 2004 DA - 2004// VL - 166 ID - Liu2004 ER - TY - JOUR TI - Stability and convergence of the difference methods for the space-time fractional advection-diffusion equation AU - F. Liu AU - P. Zhuang AU - V. Anh AU - I. Turner AU - K. Burrage JO - Appl. Math. Comput. PY - 2007 DA - 2007// VL - 191 ID - Liu2007 ER - TY - BOOK TI - Numerical methods of fractional partial differential equations and their applications AU - F. Liu AU - P. Zhuang AU - Q.-X. Liu PB - Science Press PY - 2015 DA - 2015// CY - (In Chinease) ID - Liu2015 ER - TY - JOUR TI - Fractional linear multistep methods for Abel-Volterra integral equations of the second kind AU - C. Lubich JO - Math. Comput. PY - 1985 DA - 1985// VL - 45 ID - Lubich1985 ER - TY - JOUR TI - Discretized fractional calculus AU - C. Lubich JO - SIAM J. Math. Anal. PY - 1986 DA - 1986// VL - 17 ID - Lubich1986 ER - TY - JOUR TI - Fractional calculus in bioengineering AU - R. L. Magin JO - Critical Reviews in Biomedical Engineering PY - 2004 DA - 2004// VL - 32 ID - Magin2004 ER - TY - JOUR TI - Finite difference approximations for fractional advection-dispersion equations AU - M. M. Meerschaert AU - C. Tadjeran JO - J. Comput. Appl. Math. PY - 2004 DA - 2004// VL - 172 ID - Meerschaert2004 ER - TY - BOOK TI - Fractional Differential Equations AU - I. Podlubny PB - Academic Press PY - 1999 DA - 1999// CY - New York ID - Podlubny 1999 ER - TY - JOUR TI - A new fractional model for giving up smoking dynamics AU - J. Singh AU - D. Kumar AU - M. A. Qurashi AU - D. Baleanu JO - Adv. Difference Equ. PY - 2017 DA - 2017// VL - 2017 ID - Singh2017 ER - TY - JOUR TI - A Novel Numerical Approach for a Nonlinear Fractional Dynamical Model of Interpersonal and Romantic Relationships AU - J. Singh AU - D. Kumar AU - M. A. Qurashi AU - D. Baleanu JO - Entropy PY - 2017 DA - 2017// VL - 2017 ID - Singh2017 ER - TY - JOUR TI - Linear approximation of transfer function with a pole of fractional order AU - H. H. Sun AU - A. Abdelwahab AU - B. Onaral JO - IEEE Trans. Automat. Contr. PY - 1984 DA - 1984// VL - 29 ID - Sun1984 ER - TY - JOUR TI - Application of positive reality principle to metal electrode linear polarization phenomena AU - H. H. Sun AU - B. Onaral AU - Y. Tsao JO - IEEE. Trans. Biomed. Eng. PY - 1984 DA - 1984// VL - 31 ID - Sun1984 ER - TY - JOUR TI - Fractional theory for transport in disordered semiconductors AU - V. V. Uchaikin AU - R. T. Sibatov JO - Commun. Nonlinear Sci. Numer. Simul. PY - 2008 DA - 2008// VL - 13 ID - Uchaikin2008 ER - TY - JOUR TI - Lattice fractional diffusion equation in terms of a Riesz-Caputo difference AU - G.-C. Wu AU - D. Baleanu AU - Z.-G. Deng AU - S.-D. Zeng JO - Phys. A PY - 2015 DA - 2015// VL - 438 ID - Wu2015 ER - TY - JOUR TI - Lyapunov functions for Riemann-Liouville-like fractional difference equations AU - G.-C. Wu AU - D. Baleanu AU - W.-H. Luo JO - Appl. Math. Comput. PY - 2017 DA - 2017// VL - 314 ID - Wu2017 ER - TY - JOUR TI - Riesz Riemann-Liouville difference on discrete domains AU - G.-C. Wu AU - D. Baleanu AU - H.-P. Xie JO - Chaos PY - 2016 DA - 2016// VL - 26 ID - Wu2016 ER - TY - JOUR TI - Second-order approximations for variable order fractional derivatives: Algorithms and applications AU - X. Zhao AU - Z.-Z. Sun AU - G. E. Karniadakis JO - J. Comput. Phys. PY - 2015 DA - 2015// VL - 293 ID - Zhao2015 ER - TY - JOUR TI - Numerical methods for the variable-order fractional advection-diffusion equation with a nonlinear source term AU - P. Zhuang AU - F. Liu AU - V. Anh AU - I. Turner JO - SIAM J. Numer. Anal. PY - 2009 DA - 2009// VL - 47 ID - Zhuang2009 ER -