Analysis of reaction–diffusion system via a new fractional derivative with non-singular kernel
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[1] M. Caputo,et al. A new dissipation model based on memory mechanism , 1971 .
[2] S. Scott,et al. Coupled reaction-diffusion waves in an isothermal autocatalytic chemical system , 1993 .
[3] I. Podlubny. Fractional differential equations , 1998 .
[4] S. Liao,et al. Beyond Perturbation: Introduction to the Homotopy Analysis Method , 2003 .
[5] Shijun Liao,et al. On the homotopy analysis method for nonlinear problems , 2004, Appl. Math. Comput..
[6] Shijun Liao,et al. Comparison between the homotopy analysis method and homotopy perturbation method , 2005, Appl. Math. Comput..
[7] K. Tsuboi,et al. An analytic solution of projectile motion with the quadratic resistance law using the homotopy analysis method , 2007 .
[8] S. Liao. An optimal homotopy-analysis approach for strongly nonlinear differential equations , 2010 .
[9] S. Abbasbandy,et al. Predictor homotopy analysis method and its application to some nonlinear problems , 2011 .
[10] Shyam L. Kalla,et al. On fractional partial differential equations related to quantum mechanics , 2011 .
[12] K. Diethelm,et al. Fractional Calculus: Models and Numerical Methods , 2012 .
[13] M. El-Tawil,et al. THE Q-HOMOTOPY ANALYSIS METHOD (Q-HAM) , 2012 .
[14] Saeid Abbasbandy,et al. Determination of optimal convergence-control parameter value in homotopy analysis method , 2013, Numerical Algorithms.
[15] S. Grace,et al. The Optimal q-Homotopy Analysis Method (Oq-HAM) , 2013, BIOINFORMATICS 2013.
[16] Sunil Dutt Purohit. Solutions of Fractional Partial Differential Equations of Quantum Mechanics , 2013 .
[17] O. Iyiola. Q-HOMOTOPY ANALYSIS METHOD AND APPLICATION TO FINGERO-IMBIBITION PHENOMENA IN DOUBLE PHASE FLOW THROUGH POROUS MEDIA , 2013 .
[18] S. Abo‐Dahab,et al. A One Step Optimal Homotopy Analysis Method for Propagation of Harmonic Waves in Nonlinear Generalized Magnetothermoelasticity with Two Relaxation Times under Influence of Rotation , 2013 .
[19] Badr Saad T. Alkahtani,et al. New model of groundwater flowing within a confine aquifer: application of Caputo-Fabrizio derivative , 2015, Arabian Journal of Geosciences.
[20] Abdon Atangana,et al. On Generalized Fractional Kinetic Equations Involving Generalized Bessel Function of the First Kind , 2015 .
[21] Abdon Atangana,et al. Numerical solution for the model of RLC circuit via the fractional derivative without singular kernel , 2015 .
[22] Badr Saad T. Alkahtani,et al. Analysis of the Keller-Segel Model with a Fractional Derivative without Singular Kernel , 2015, Entropy.
[23] M. Caputo,et al. A new Definition of Fractional Derivative without Singular Kernel , 2015 .
[24] Abdon Atangana,et al. On the new fractional derivative and application to nonlinear Fisher's reaction-diffusion equation , 2016, Appl. Math. Comput..
[25] A. Alsaedi,et al. On Coupled Systems of Time-Fractional Differential Problems by Using a New Fractional Derivative , 2016 .
[26] Obaid J. Algahtani,et al. Comparing the Atangana–Baleanu and Caputo–Fabrizio derivative with fractional order: Allen Cahn model , 2016 .
[27] K. Nisar,et al. Generalized fractional kinetic equations involving generalized Struve function of the first kind , 2016 .
[28] Y. S. Hamed,et al. Solving the convection–diffusion equation by means of the optimal q-homotopy analysis method (Oq-HAM) , 2016 .
[29] José Francisco Gómez-Aguilar,et al. Modeling diffusive transport with a fractional derivative without singular kernel , 2016 .
[30] Devendra Kumar,et al. Numerical solution of time- and space-fractional coupled Burgers’ equations via homotopy algorithm , 2016 .
[31] Abdon Atangana,et al. A new nonlinear triadic model of predator–prey based on derivative with non-local and non-singular kernel , 2016 .
[32] Ilknur Koca,et al. Chaos in a simple nonlinear system with Atangana-Baleanu derivatives with fractional order , 2016 .
[33] Xiao-Jun Yang,et al. General fractional calculus operators containing the generalized Mittag-Leffler functions applied to anomalous relaxation , 2017 .
[34] José Francisco Gómez-Aguilar,et al. Space–time fractional diffusion equation using a derivative with nonsingular and regular kernel , 2017 .
[35] Sunil Kumar,et al. An efficient computational approach for time-fractional Rosenau–Hyman equation , 2017, Neural Computing and Applications.
[36] Abdon Atangana,et al. Model of Thin Viscous Fluid Sheet Flow within the Scope of Fractional Calculus: Fractional Derivative with and No Singular Kernel , 2017, Fundam. Informaticae.
[37] E. K. Lenzi,et al. The Role of Fractional Time-Derivative Operators on Anomalous Diffusion , 2017, Front. Phys..
[38] K. Saad,et al. Optimal q-homotopy analysis method for time-space fractional gas dynamics equation , 2017 .
[39] Ilknur Koca,et al. Analysis of rubella disease model with non-local and non-singular fractional derivatives , 2017 .
[40] Devendra Kumar,et al. A new analysis for fractional model of regularized long‐wave equation arising in ion acoustic plasma waves , 2017 .
[41] Syed Tauseef Mohyud-Din,et al. On linear viscoelasticity within general fractional derivatives without singular kernel , 2017 .
[42] Asifa Tassaddiq,et al. Atangana-Baleanu and Caputo Fabrizio Analysis of Fractional Derivatives for Heat and Mass Transfer of Second Grade Fluids over a Vertical Plate: A Comparative Study , 2017, Entropy.
[43] Hari M. Srivastava,et al. General fractional-order anomalous diffusion with non-singular power-law kernel , 2017 .
[44] Devendra Kumar,et al. An efficient analytical technique for fractional model of vibration equation , 2017 .
[45] Dumitru Baleanu,et al. Relaxation and diffusion models with non-singular kernels , 2017 .
[46] D. Vieru,et al. Modeling electro-magneto-hydrodynamic thermo-fluidic transport of biofluids with new trend of fractional derivative without singular kernel , 2017 .
[47] Abdon Atangana,et al. Solutions of Cattaneo-Hristov model of elastic heat diffusion with Caputo-Fabrizio and Atangana-Baleanu fractional derivatives , 2017 .
[48] S. Manjarekar,et al. Generalized Elzaki – Tarig Transformation and its Applications to New Fractional Derivative with Non Singular Kernel , 2017 .
[49] José Francisco Gómez-Aguilar,et al. Irving–Mullineux oscillator via fractional derivatives with Mittag-Leffler kernel , 2017 .
[50] A. Atangana,et al. Analysis of a new model of H1N1 spread: Model obtained via Mittag-Leffler function , 2017 .
[51] K. Saad,et al. New fractional derivatives applied to the Korteweg–de Vries and Korteweg–de Vries–Burger’s equations , 2018 .
[52] J. F. Gómez‐Aguilar,et al. Decolonisation of fractional calculus rules: Breaking commutativity and associativity to capture more natural phenomena , 2018 .
[53] Khaled M. Saad,et al. Comparing the Caputo, Caputo-Fabrizio and Atangana-Baleanu derivative with fractional order: Fractional cubic isothermal auto-catalytic chemical system , 2018 .
[54] José Francisco Gómez-Aguilar,et al. A numerical solution for a variable-order reaction–diffusion model by using fractional derivatives with non-local and non-singular kernel , 2018 .
[55] Dumitru Baleanu,et al. Analysis of regularized long-wave equation associated with a new fractional operator with Mittag-Leffler type kernel , 2018 .
[56] Abdon Atangana,et al. Non validity of index law in fractional calculus: A fractional differential operator with Markovian and non-Markovian properties , 2018, Physica A: Statistical Mechanics and its Applications.