A new fractional model and optimal control of a tumor-immune surveillance with non-singular derivative operator

2007, An evolutionary hybrid cellular automaton model of solid tumour growth, J. Theor. Biol., 246, 583, 10.1016/j.jtbi.2007.01.027

2006, Mathematical modelling of radiotherapy strategies for early breast cancer, J. Theor. Biol., 241, 158, 10.1016/j.jtbi.2005.11.015

2005, A validated mathematical model of cell-mediated immune response to tumour growth, Cancer Res., 65, 7950, 10.1158/0008-5472.CAN-05-0564

2007, Chemotherapy for tumors: An analysis of the dynamics and a study of quadratic and linear optimal controls, Math. Biosci., 209, 292, 10.1016/j.mbs.2006.05.003

2012, Evasion of tumours from the control of the immune system: Consequences of brief encounters, Biol. Direct., 7, 1, 10.1186/1745-6150-7-1

2016, Mathematical model of tumor-immune surveillance, J. Theor. Biol., 404, 312, 10.1016/j.jtbi.2016.06.012

2014, Periodic and chaotic oscillations in a tumor and immune system interaction model with three delays, Chaos, 24, 023101, 10.1063/1.4870363

2015, Optimal Control for Mathematical Models of Cancer Therapies

2013, Parameter estimation and optimal scheduling algorithm for a mathematical model of intermittent androgen suppression therapy for prostate cancer, Chaos, 23, 043125, 10.1063/1.4833455

2017, Reinforcement learning-based control of drug dosing for cancer chemotherapy treatment, Math. Biosci., 293, 11, 10.1016/j.mbs.2017.08.004

2017, Adaptive robust control of cancer chemotherapy with extended Kalman filter observer, Inf. Med. Unlocked, 8, 1, 10.1016/j.imu.2017.03.002

2018, Optimal duration and dosage of BCG intravesical immunotherapy: A free final time optimal control approach, Math. Meth. Appl. Sci., 41, 2209, 10.1002/mma.4745

2016, A mixed radiotherapy and chemotherapy model for treatment of cancer with metastasis, Math. Method. Appl. Sci., 39, 4603, 10.1002/mma.3887

2016, Analysis of the dynamics of a tumor-immune system with chemotherapy and immunotherapy and quadratic optimal control, Differ. Equ. Dyn. Syst., 24, 149, 10.1007/s12591-015-0250-1

2016, Fractional formalism to DNA chain and impact of the fractional order on breather dynamics, Chaos, 26, 123120, 10.1063/1.4972405

2017, The role of fractional calculus in modeling biological phenomena: A review, Commun. Nonlinear Sci., 51, 141, 10.1016/j.cnsns.2017.04.001

2018, A new collection of real world applications of fractional calculus in science and engineering, Commun. Nonlinear Sci., 64, 213, 10.1016/j.cnsns.2018.04.019

2013, Numerical modeling of fractional-order biological systems, Abstr. Appl. Anal., 2013, 816803, 10.1155/2013/816803

2018, HIV/HCV coinfection model: A fractional-order perspective for the effect of the HIV viral load, Adv. Differ. Equ., 2018, 1, 10.1186/s13662-017-1452-3

2019, Time-varying pharmacodynamics in a simple non-integer HIV infection model, Math. Biosci., 307, 1, 10.1016/j.mbs.2018.11.001

2018, Fractional dynamics of an infection model with time-varying drug exposure, J. Comput. Nonlin. Dyn., 13, 090904, 10.1115/1.4038643

2013, Fractional model for malaria transmission under control strategies, Comput. Math. Appl., 66, 908, 10.1016/j.camwa.2012.11.017

2016, On the optimal control for fractional multi-strain TB model, Optim. Contr. Appl. Met., 37, 1355, 10.1002/oca.2247

2017, Legendre spectral-collocation method for solving fractional optimal control of HIV infection of CD4+ T cells mathematical model, J. Def. Model. Simul., 14, 273, 10.1177/1548512916677582

2016, Computational methods for the fractional optimal control HIV infection, J. Fract. Calc. Appl., 7, 121

2018, Optimal control for a nonlinear mathematical model of tumor under immune suppression: A numerical approach, Optim. Contr. Appl. Met., 39, 1581, 10.1002/oca.2427

2018, A new fractional analysis on the interaction of HIV with CD4+ T-cells, Chaos Soliton. Fract., 113, 221, 10.1016/j.chaos.2018.06.009

2015, A new definition of fractional derivative without singular kernel, Progr. Fract. Differ. Appl., 1, 73

2016, New fractional derivatives with nonlocal and non-singular kernel: Theory and application to heat transfer model, Therm. Sci., 20, 763, 10.2298/TSCI160111018A

2019, The failure of certain fractional calculus operators in two physical models, Fract. Calc. Appl. Anal., 22, 255, 10.1515/fca-2019-0017

2018, Two-strain epidemic model involving fractional derivative with Mittag-Leffler kernel, Chaos, 28, 123121, 10.1063/1.5074084

2019, New idea of Atangana, Baleanu fractional derivatives to human blood flow in nanofluids, Chaos, 29, 013121, 10.1063/1.5078738

2019, On the formulation of Adams-Bashforth scheme with Atangana-Baleanu-Caputo fractional derivative to model chaotic problems, Chaos, 29, 023111, 10.1063/1.5085490

2019, Fractional modeling of blood ethanol concentration system with real data application, Chaos, 29, 013143, 10.1063/1.5082907

2007, Functional Fractional Calculus for System Identification and Controls

1993, Fractional Integrals and Derivatives: Theory and Applications

2017, On the analysis of chemical kinetics system pertaining to a fractional derivative with Mittag-Leffler type kernel, Chaos, 27, 103113, 10.1063/1.4995032

2018, Fractional derivatives with no-index law property: Application to chaos and statistics, Chaos Soliton. Fract., 114, 516, 10.1016/j.chaos.2018.07.033

2018, Analysis of reaction-diffusion system via a new fractional derivative with non-singular kernel, Physica A, 509, 703, 10.1016/j.physa.2018.05.137

2018, The role of power decay, exponential decay and Mittag–Leffler function’s waiting time distribution: Application of cancer spread, Physica A, 512, 330, 10.1016/j.physa.2018.08.033

2018, New fractional derivatives with non-singular kernel applied to the Burgers equation, Chaos, 28, 063109, 10.1063/1.5026284

1994, Nonlinear dynamics of immunogenic tumors: Parameter estimation and global bifurcation analysis, B. Math. Biol., 56, 295, 10.1007/BF02460644

2006, Mixed immunotherapy and chemotherapy of tumors: Modeling, applications and biological interpretations, J. Theor. Biol., 238, 841, 10.1016/j.jtbi.2005.06.037

2003, A mathematical model of immune response to tumor invasion, Comput. Fluid Solid Mech., 2003, 1661, 10.1016/B978-008044046-0.50404-8

2013, A fractional calculus based model for the simulation of an outbreak of dengue fever, Nonlinear Dynam., 71, 613, 10.1007/s11071-012-0475-2

2013, The finite difference methods for fractional ordinary differential equations, Numer. Func. Anal. Opt., 34, 149, 10.1080/01630563.2012.706673

2016, An extended predictor-corrector algorithm for variable-order fractional delay differential equations, J. Comput. Nonlin. Dyn., 11, 061001, 10.1115/1.4032574

2017, Analysis and application of new fractional Adams–Bashforth scheme with Caputo–Fabrizio derivative, Chaos Soliton. Fract., 105, 111, 10.1016/j.chaos.2017.10.020

2018, On the nonlinear dynamical systems within the generalized fractional derivatives with Mittag–Leffler kernel, Nonlinear Dynam., 94, 397, 10.1007/s11071-018-4367-y

2010, Fractional optimal control problems with specified final time, J. Comput. Nonlin. Dyn., 6, 1, 10.1115/1.4002508

2019, New aspects of time fractional optimal control problems within operators with nonsingular kernel, Discrete Cont. Dyn. S, 10.3934/dcdss.2020023

2017, A new formulation of the fractional optimal control problems involving Mittag–Leffler nonsingular kernel, J. Optimiz. Theory App., 175, 718, 10.1007/s10957-017-1186-0

2017, A self-adaptive intelligence gray prediction model with the optimal fractional order accumulating operator and its application, Math. Method Appl. Sci., 40, 7843, 10.1002/mma.4565