
AIMS Mathematics, 2020, 5(2): 15191531. doi: 10.3934/math.2020104
Research article Special Issues
Export file:
Format
 RIS(for EndNote,Reference Manager,ProCite)
 BibTex
 Text
Content
 Citation Only
 Citation and Abstract
Investigating of an immune systemcancer mathematical model with MittagLeffler kernel
Department of Mathematics, Faculty of Science and Arts, Balıkesir University, Turkey
Received: , Accepted: , Published:
Special Issues: Recent Advances in Fractional Calculus with Real World Applications
References
1. L. Marsha, K. R. Conroy, J. L. Davis, et al. Atlas Pathophysiology, Lippincott Williams & Wilkins, 2010.
2. V. Kumar, A. Abbas, J. Aster, Robbins and cotran pathologic basis of disease, Canada: Elsevier, 2014.
3. M. Zanetti, Tapping CD4 T cells for cancer immunotherapy: The choice of personalized genomics, J. Immunol., 194 (2015), 20492056.
4. D. Cassell, J. Forman, Linked recognition of helper and cytotoxic antigenic determinants for he generation of cytotoxic T lymphocytes, Ann. N. Y. Acad. Sci., 532 (1998), 5160.
5. H. Choudhry, N. Helmi, W. H. Abdulaal, et al. Prospects of IL2 in cancer immunotherapy, BioMed Res. Int., 2018 (2018), 9056173.
6. A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations, Elsevier, 2006.
7. D. Baleanu, K. Diethelm, E. Scalas, et al. Fractional calculus models and numerical methods, World Scientific, 2012
8. N. Özdemir, D. Karadeniz, B. B. Iskender, Fractional optimal control problem of a distributed system in cylindrical coordinates, Phys. Lett. A, 373 (2009), 221226.
9. F. Evirgen, N. Özdemir, Multistage adomian decomposition method for solving NLP problems over a nonlinear fractional dynamical system, J. Comput. Nonlinear Dyn., 6 (2011), 21003.
10. F. Evirgen, Analyze the optimal solutions of optimization problems by means of fractional gradient based system using VIM, An International Journal of Optimization and Control: Theories & Applications (IJOCTA), 6 (2016), 7583.
11. Z. Hammouch, T. Mekkaoui, Circuit design and simulation for the fractionalorder chaotic behavior in a new dynamical system, Complex Intell. Syst., 4 (2018), 251260.
12. E. Bonyah, A. Atangana, M. A. Khan, Modeling the spread of computer virus via Caputo fractional derivative and the beta derivative, Asia Pacific Journal on Computational Engineering, 4 (2017), 115.
13. N. Özdemir, M. Yavuz, Numerical solution of fractional BlackScholes equation by using the multivariate pade approximation, Acta Phys. Pol. A., 132 (2017), 10501053.
14. E. Uçar, N. Özdemir, E. Altun, Fractional order model of immune cells influenced by cancer cells, Math. Model. Nat. Phenom., 14 (2019), 308.
15. A. Atangana, D. Baleanu, New fractional derivatives with nonlocal and nonsingular kernel: theory and applications to heat transfer model, Therm. Sci., 20 (2016), 763769.
16. M. Yavuz, N. Özdemir, H. M. Baskonus, Solutions of partial differential equations using the fractional operator involving MittagLeffler kernel, Eur. Phys. J. Plus, 133 (2018), 215.
17. V. F. MoralesDelgadoa, J. F. GomezAguilar, M. A. TanecoHernandez, et al. Mathematical modeling of the smoking dynamics using fractional differential equations with local and nonlocal kernel, J. Nonlinear Sci. Appl., 11 (2018), 9941014.
18. N. A. Asif, Z. Hammouch, M. B. Riaz, et al. Analytical solution of a Maxwell fluid with slip effects in view of the CaputoFabrizio derivative, Eur. Phys. J. Plus, 133 (2018), 272.
19. I. Koca, Analysis of rubella disease model with nonlocal and nonsingular fractional derivatives, Int. J. Optim. Control Theor. Appl. IJOCTA, 8 (2018), 1725.
20. D. Avcı A. Yetim, Analytical solutions to the advectiondiffusion equation with the AtanganaBaleanu derivative over a finite domain, J. BAUN Inst. Sci. Technol., 20 (2018), 382395.
21. S. Uçar, E. Uçar, N. Özdemir, et al. Mathematical analysis and numerical simulation for a smoking model with AtanganaBaleanu derivative, Chaos, Solitons & Fractals, 118 (2019), 300306.
22. D. Baleanu, A. Fernandez, On some new properties of fractional derivatives with MittagLeffler kernel, Commun. Nonlinear Sci. Numer. Simulat., 59 (2018), 444462.
23. A. Fernandez, D. Baleanu, H. M. Srivastava, Series representations for fractionalcalculus operators involving generalised MittagLeffler functions, Commun. Nonlinear Sci. Numer. Simulat., 67 (2019), 517527.
24. S. Uçar, Existence and uniqueness results for a smoking model with determination and education in the frame of nonsingular derivatives, Discrete Continuous Dyn. Syst. Ser. S, in press.
25. F. Evirgen, S. Uçar, N. Özdemir, et al. System response of an alcoholism model under the effect of immigration via nonsingular kernel derivative, Discrete Continuous Dyn. Syst. Ser. S, in press.
26. J. E. SolisPerez, J. F. GomezAguilar, A. Atangana, A factional mathematical model of breast cancer competition model, Chaos, Solitons and Fractals, 127 (2019), 3854.
27. V. F. MoralesDelgado, J. F. GomezAguilar, K. Saad, et al. Application of the CaputoFabrizio and AtanganaBaleanu fractional derivatives to mathematical model of cancer chemotherapy effect, Math. Methods Appl. Sci., 42 (2019), 11671193.
28. P. Vereesha, D. G. Prakasha, H. M. Baskonus, New numerical surfaces to the mathematical model of cancer chemotherapy effect in Caputo fractional derivatives, CHAOS, 29 (2019), 113.
29. A. Minelli, F. Topputo, F. Bernelli, Controlled drug delivery in cancer immunotherapy: Stability, optimization and monte carlo analysis, SIAM J. Appl. Math., 71 (2011), 22292245.
30. L. G. De Pillis, A. Radunskaya, A mathematical tumour model with immune resistance and drug therapy: An optimal control approach, Journal of Theoretical Medicine, 3 (2001), 79100.
31. F. Castiglione, B. Piccoli, Cancer immunotheraphy, mathematical modeling and optimal control, J. Theor. Biol., 247 (2007), 723732.
32. D. Baleanu, A. Jajarmi, M. Hajipour, On the nonlinear dynamical systems within the generalized fractional derivatives with MittagLeffler kernel, Nonlinear Dyn., 94 (2018), 397414.
© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)