Application of the Caputo‐Fabrizio and Atangana‐Baleanu fractional derivatives to mathematical model of cancer chemotherapy effect

[1]  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.

[2]  Ahmed Gomaa Radwan,et al.  Fractional-order mathematical model for Chronic Myeloid Leukaemia , 2017, 2017 European Conference on Circuit Theory and Design (ECCTD).

[3]  Philip Hahnfeldt,et al.  A Multicompartment Mathematical Model of Cancer Stem Cell-Driven Tumor Growth Dynamics , 2014, Bulletin of mathematical biology.

[4]  Obaid J. Algahtani,et al.  Comparing the Atangana–Baleanu and Caputo–Fabrizio derivative with fractional order: Allen Cahn model , 2016 .

[5]  Manmohan Singh,et al.  Modelling of tumor cells regression in response to chemotherapeutic treatment , 2017 .

[6]  Abbas Saadatmandi,et al.  Bernstein operational matrix of fractional derivatives and its applications , 2014 .

[7]  Arnan Mitchell,et al.  An Investigation on Platelet Transport during Thrombus Formation at Micro-Scale Stenosis , 2013, PloS one.

[8]  A. Atangana,et al.  Analysis of exact groundwater model within a confined aquifer: New proposed model beyond the Theis equation , 2018, The European Physical Journal Plus.

[9]  Abdon Atangana,et al.  Tumour model with intrusive morphology, progressive phenotypical heterogeneity and memory , 2018 .

[10]  J. F. Gómez‐Aguilar,et al.  Decolonisation of fractional calculus rules: Breaking commutativity and associativity to capture more natural phenomena , 2018 .

[11]  Avner Friedman,et al.  A mathematical model for pancreatic cancer growth and treatments. , 2014, Journal of theoretical biology.

[12]  Z. Vosika,et al.  Fractional Calculus Model of Electrical Impedance Applied to Human Skin , 2013, PloS one.

[13]  Kirti Arekar,et al.  Study of Bergman’s minimal blood glucose-insulin model by adomian decomposition method , 2017 .

[14]  Ilknur Koca,et al.  Chaos in a simple nonlinear system with Atangana-Baleanu derivatives with fractional order , 2016 .

[15]  O. Iyiola,et al.  Generalised homotopy analysis method (q-HAM) for solving foam drainage equation of time fractional type , 2013 .

[16]  Dumitru Baleanu,et al.  Laplace homotopy analysis method for solving linear partial differential equations using a fractional derivative with and without kernel singular , 2016 .

[17]  F. Haq,et al.  Numerical Solution of Fractional Order Epidemic Model of a Vector Born Disease by Laplace Adomian Decomposition Method , 2017 .

[18]  Bernardo Spagnolo,et al.  Nonlinear Relaxation Phenomena in Metastable Condensed Matter Systems , 2016, Entropy.

[19]  Bart Koopman,et al.  The effect of tyre and rider properties on the stability of a bicycle , 2015 .

[20]  Saif Ullah,et al.  Modeling and analysis of the fractional HBV model with Atangana-Baleanu derivative , 2018, The European Physical Journal Plus.

[21]  Dumitru Baleanu,et al.  A new approach for the nonlinear fractional optimal control problems with external persistent disturbances , 2018, J. Frankl. Inst..

[22]  Kristen Abernathy,et al.  Global Dynamics of a Breast Cancer Competition Model , 2017, Differential Equations and Dynamical Systems.

[23]  Sunil Kumar,et al.  New analytical method for gas dynamics equation arising in shock fronts , 2014, Comput. Phys. Commun..

[24]  Ivo Petráš,et al.  Simulation of Drug Uptake in a Two Compartmental Fractional Model for a Biological System. , 2011, Communications in nonlinear science & numerical simulation.

[25]  Ignacio A. Rodriguez-Brenes,et al.  Mathematical Modeling of Normal and Cancer Stem Cells , 2017, Current Stem Cell Reports.

[26]  G. Losa On the Fractal Design in Human Brain and Nervous Tissue , 2014 .

[27]  Abdon Atangana,et al.  Solutions of Cattaneo-Hristov model of elastic heat diffusion with Caputo-Fabrizio and Atangana-Baleanu fractional derivatives , 2017 .

[28]  D. Baleanu,et al.  Suboptimal control of fractional-order dynamic systems with delay argument , 2018 .

[29]  R. Magin,et al.  Characterization of Anomalous Diffusion in Porous Biological Tissues Using Fractional Order Derivatives and Entropy. , 2013, Microporous and mesoporous materials : the official journal of the International Zeolite Association.

[30]  S. Manjarekar,et al.  Generalized Elzaki – Tarig Transformation and its Applications to New Fractional Derivative with Non Singular Kernel , 2017 .

[31]  T. Abdeljawad,et al.  STABILITY ANALYSIS OF A FRACTIONAL ORDER DIFFERENTIAL EQUATIN MODEL OF A BRAIN TUMOR GROWTH DEPENDING ON THE DENSITY , 2015 .

[32]  Y. S. Hamed,et al.  Solving the convection–diffusion equation by means of the optimal q-homotopy analysis method (Oq-HAM) , 2016 .

[33]  Abdon Atangana,et al.  The role of power decay, exponential decay and Mittag-Leffler function’s waiting time distribution: Application of cancer spread , 2018, Physica A: Statistical Mechanics and its Applications.

[34]  M. Dehghan,et al.  Solving nonlinear fractional partial differential equations using the homotopy analysis method , 2010 .

[35]  K. Saad,et al.  New fractional derivatives applied to the Korteweg–de Vries and Korteweg–de Vries–Burger’s equations , 2018 .

[36]  J. F. Gómez‐Aguilar,et al.  Analysis of reaction–diffusion system via a new fractional derivative with non-singular kernel , 2018, Physica A: Statistical Mechanics and its Applications.

[37]  Saeid Abbasbandy,et al.  Analytical solution of fractional Navier–Stokes equation by using modified Laplace decomposition method , 2014 .

[38]  Dumitru Baleanu,et al.  Modified Kawahara equation within a fractional derivative with non-singular kernel , 2017 .

[39]  Hossein Jafari,et al.  Homotopy analysis method for solving linear and nonlinear fractional diffusion-wave equation , 2009 .

[40]  Sunil Kumar,et al.  A new analytical modelling for fractional telegraph equation via Laplace transform , 2014 .

[41]  S. Momani,et al.  The homotopy analysis method for handling systems of fractional differential equations , 2010 .

[42]  Mahmoud S. Rawashdeh,et al.  The fractional natural decomposition method: theories and applications , 2017 .

[43]  Dumitru Baleanu,et al.  New fractional derivatives with non-singular kernel applied to the Burgers equation. , 2018, Chaos.

[44]  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.

[45]  Zaid Odibat,et al.  An adaptation of homotopy analysis method for reliable treatment of strongly nonlinear problems: construction of homotopy polynomials , 2015 .

[46]  P. Zegeling,et al.  A homotopy perturbation method for fractional-order advection-diffusion-reaction boundary-value problems , 2017 .

[47]  Richard L. Magin,et al.  Fractional calculus models of complex dynamics in biological tissues , 2010, Comput. Math. Appl..

[48]  Abdon Atangana,et al.  A new nonlinear triadic model of predator–prey based on derivative with non-local and non-singular kernel , 2016 .

[49]  José Francisco Gómez-Aguilar,et al.  Irving–Mullineux oscillator via fractional derivatives with Mittag-Leffler kernel , 2017 .

[50]  Saeid Abbasbandy,et al.  On convergence of homotopy analysis method and its application to fractional integro-differential equations , 2013 .

[51]  Sunil Kumar,et al.  A new analysis for the Keller-Segel model of fractional order , 2017, Numerical Algorithms.

[52]  Abdon Atangana,et al.  Numerical approximation of nonlinear fractional parabolic differential equations with Caputo-Fabrizio derivative in Riemann-Liouville sense , 2017 .

[53]  M. Caputo,et al.  A new Definition of Fractional Derivative without Singular Kernel , 2015 .

[54]  Dumitru Baleanu,et al.  A new fractional analysis on the interaction of HIV withCD4+T-cells , 2018, Chaos, Solitons & Fractals.

[55]  Ghaus ur Rahman,et al.  Numerical solution of fractional order smoking model via laplace Adomian decomposition method , 2017, Alexandria Engineering Journal.

[56]  Dumitru Baleanu,et al.  A new method for investigating approximate solutions of some fractional integro-differential equations involving the Caputo-Fabrizio derivative , 2017 .

[57]  Dumitru Baleanu,et al.  Analysis of regularized long-wave equation associated with a new fractional operator with Mittag-Leffler type kernel , 2018 .

[58]  A. Atangana,et al.  New Fractional Derivatives with Nonlocal and Non-Singular Kernel: Theory and Application to Heat Transfer Model , 2016, 1602.03408.

[59]  Chris Yakopcic,et al.  A Computational Study and Stability Analysis of a Mathematical Model for In Vitro Inhibition of Cancer Cell Mutation , 2017 .

[60]  Devendra Kumar,et al.  Analysis of an El Nino-Southern Oscillation model with a new fractional derivative , 2017 .

[61]  F. Ghasemi,et al.  Laser-assisted generation of periodic structures on a steel surface: A method for increasing microhardness , 2018 .

[62]  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 .

[63]  Gianluca Danilo D'Urso,et al.  Micro-electro discharge machining drilling of stainless steel with copper electrode: The influence of process parameters and electrode size , 2016 .

[64]  Devendra Kumar,et al.  A modified homotopy analysis method for solution of fractional wave equations , 2015 .