[1] R. Hilfer, Applications of Fractional Calculus in Physics",World Scientific, Singapore, 2000.
[2] A.A. Kilbas, O.I. Marichev, S.G. Samko, Fractional Integrals and Derivatives (Theory and Applications)",
Gordon and Breach, Switzerland, 1993.
[3] A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations", North
Holland Mathematics Studies, vol. 204, Elseveir, Amsterdam, 2006
[4] K.S. Miller, B. Ross, \An Introduction to the Fractional Calculus and Fractional Differential Equations", Wiley,
New York, 1993.
[5] C. Goodrich, Existence of a positive solution to a class of Fractional differential equations," Comput. Math.
Appl., 59 (2010) 3889-3999.
[6] P. Rahimkhani, Y. Ordokhani, E. Babolian, Numerical solution of fractional pantograph differential equations
by using generalized fractional-order Bernoulli wavelet", J. Comput. Appl. Math., 493-510 (2017).
[7] U. Saeed, M.ur. Rehman, Hermite wavelet method for fractional delay differential equations", J. Differ. Eqn.
(2014).
[8] Y. Yang, Y. Huang, Spectral-collocation methods for fractional pantograph delay integro differential equations",
Adv. Math. Phys. (2013).
[9] M.K. Ishteva, properties and application of the Caputo Fractional operator", Deptt. Math. Univ. Karlsruhe,
2005.
[10] Y. Zhou, Basic theory of fractional di erential equations", world scientific publishing. USA, 1964.
[11] A. Ali, K. Shah, R.A. Khan Existence of positive solution to a class of boundary value problems of fractional
di erential equations", Compu. Methods Diff. Equ. 19-29 (2016).
[12] A. Ali et al. Existence and stability of solution to a toppled systems of differential equations of non-integer
order", Bound. Value. Probl. 2017 (2017).
[13] M. Caputo, Linear Models of dissipation whose Q is almost frequency independent", Int. Jou. Geo. Sci. 529-539.
(1967)
[14] V. Lakshmikantham, S. Leela, J. Vasundhara, Theory of Fractional Dynamic Systems", Cambridge Academic
Publishers, Cambridge, UK, 2009.
[15] Cai, L. Wu, Analysis of an HIV/AIDS treatment model with a nonlinear incidence rate", Chaos. Soliton. Frat.
175-182. (2009)
[16] R.C. Wu, X.D. Hei, L.P. Chen, Finite-time stability of fractional-order neural networks with delay", Commun.
Theor. Phys. 189-193 2013.
[17] A. Nanware, D.B. Dhaigude, Existence and uniqueness of solutions of differential equations of fractional order
with integral boundary conditions", J. Nonlinear Sci. Appl. 246-254 2014.
[18] R.P. Agarwal, M. Belmekki, M. Benchohra, A survey on semilinear differential equations and inclusions involving
Riemann-Liouville fractional derivative", Adv. Differ. Equ. 2009.
[19] J.C. Trigeassou, A Lyapunov approach to the stability of fractional differential equations", Signal Process,
437-445 (2011).
[20] G. Lijun, D.Wang, G.Wang, Further results on exponential stability for impulsive switched nonlinear time-delay
systems with delayed impulse effects", Appl. Math. Comput. 186-200 2015.
[21] I. Stamova, Mittag-Leffer stability of impulsive di erential equations of fractional order", Q. Appl. Math. 525-
535 2015.
[22] S.M. Ullam, Problems in Modern Mathematics", Science Editors, Wiley, New York 1940.
[23] D.H. Hyers, On the stability of the linear functional equation", Proc. Natl. Acad. Sci. 222-224 (1941).
[24] S.M. Ulam, Problems in Modern Mathematics", Wiley, New York, 1940. 1
[25] S.M. Ulam, A Collection of Mathematical Problems", Interscience, New York, 1960. 1
[26] T.M. Rassias, On the stability of the linear mapping in Banach spaces", Proc. Am. Math. Soc. 297-300 (1978).
1
[27] M. Benchohra, S. Hamani, S.K. Ntouyas, Boundary value problems for differential equations with fractional
order and nonlocal conditions", J. Nonl. Anal. 2391-2396 (2009). 1, 2.3
[28] K. Shah, R.A. Khan, Existence and uniqueness of positive solutions to a coupled system of nonlinear fractional
order di erential equations with anti periodic boundary conditions", Di er. Equ. Appl. 245-262 (2015). 1
[29] R.A. Khan, K. Shah, Existence and uniqueness of solutions to fractional order multi-point boundary value
problems", Commun. Appl. Anal. 515-526 (2015). 1
[30] A. Atangana, D. Baleanu, New fractional derivatives with nonlocal and non-singular kernel", Theor, Appl. Heat
Transfer Model, Thermal Science. 763-769. (2016). 1, 2.1
[31] J.D. Djida, A. Atangana, I. Area, Numerical computation of a fractional derivative with non-local and non-
singular kernel", Math. Model. Nat. Phenomena. 4-13 (2017). 1, 2.1
[32] O. Algahtani, Comparing the Atangana-Baleanu and Caputo-Fabrizio derivative with fractional order Allen
Cahn model", Chaos Solitons Fractals (2016). 1, 2.1
[33] D. Kumar, J. Singh, S. Kumar, Numerical computation of fractional multi-dimensional diffusion equations by
using a modiffed homotopy perturbation method", J. Assoc. Arab. Univ. Basic. Appl. Sci., 20-26 (2015). 1
[34] S. Yanga, A. Xiao, H. Su, Convergence of the variational iteration method for solving multi-order fractional
di erential equations", Comput. Math. Appl., 2871-2879 (2010). 1
[35] Z. Odibat and S. Momani, A generalized differential transform method for linear partial differential equations
of fractional order", Appl. Math. Lett. , 194-199 (2008).
[36] M. Deghan, Y.A. Yousef, A. Lotfi, The use of He's variational iteration method for solving the telegraph and
fractional telegraph equations", Int. J. Numer. Methods Biomed. Eng., 219-231 (2011). 1
[37] P. Zhou, et al. A pneumonia outbreak associated with a new coronavirus of probable bat origin", Nature 270-273
(2020). 1
[38] World Health Organization, Coronavirus disease 2019 (COVID-19): Situation Report", 21 April, 2020. 1
[39] L. Edelstein-Keshet, \Mathematical models in biology. Society for Industrial and Applied Mathematics", 2005.
1
[40] C.A.A. Beauchemin , H. Andreas, A review of mathematical models of in uenza A infections within a host or
cell culture: lessons learned and challenges ahead", BMC public health (2011). 1
[41] Brauer, Fred, Ven den Driessche, J. Wu, Lecture notes in mathematical epidemiology", Berlin, Germany,
Springer, 2008. 1
[42] LA. Rvachev, M. Ira, Jr. Longini, A mathematical model for the global spread of in uenza", Mathematical
biosciences 3-22 (1985). 1
[43] J.D Murray, Mathematical biology: An Introduction", Springer Science and Business Media, Vol. 17. 2007. 1
[44] J. Biazar, Solution of the epidemic model by Adomian decomposition method", App. Math. comput., 1101-1106
(2006). 1
[45] K. Shah et al, Semi-analytical study of Pine Wilt Disease model with convex rate under Caputo-Fabrizio
fractional order derivative", Chaos. Sol. Frac. (2020). 1
[46] A. Abdilraze, D. Pelinosky, Convergence of the Adomian Decomposition method for initial value problems",
Num. Methods. Part. Di . Equ. 749-766 (2009). 1
[47] A. Naghipour, J. Manafan, Application of the Laplace adomian decomposition method and implicit methods
for solving Burger's equation", TWMS J. Pure. Apple. Math. 68-77 (2015). 1
[48] K. Shah, H. Khalil, R.A. Khan, Analytical solutions of fractional order diffusion equations by Natural transform
method", Iran J. Sci. Technol. Trans. Sci. (2016). 1
[49] D.W. Jordan, P. Smith, Nonlinear Ordinary Differential Equations", third ed., Oxford University Press, (1999).
1
[50] P. Palese, J.F. Young, Variation of in uenza A, B, and C viruses", Science, 215, 1468-1474 (1982). 1
[51] R. Anderson, R. May, Infectious Disease of Humans", Dynamics and Control, Oxford University Press, Oxford,
UK, (1995). 1
[52] R.G. Webster, W.J. Bean, O.T. Gorman, T.M. Chambers, Y. Kawaoka, \Evolution and ecology of in uenza A
viruses", Microbiological Reviews, 56, 152-179 (1992). 1
[53] R. Casagrandi, L. Bolzoni, S.A. Levin, V. Andreasen, The SIRC model and the in uenza A", Mathematical
Biosciences, 2002, 152-169 2006. 1
[54] G.P. Samanta, Global dynamic of nonautonomous SIRC model and in uenza A with distributed time delay",
Di erential Equations and Dynamical Systems, 18(4), 341-362 (2010). 1
[55] W.O. Kermack, A.G. McKendrick, Contributions to the mathematical theory of epidemics", Proceedings of
Royal Society of London, 115, 700-721 (1927). 1
[56] H. Li, S. Guo, Dynamic of a SIRC epidemiological model", Electronic journal of Differential equations, 2017(121),
1-18 (2017). 1
[57] K. Shah, F. Jarad and T. Abdeljawad, On a nonlinear fractional order model of dengue fever disease under
Caputo-Fabrizo derivative", Alexandria Engineering Journal (2020). 5.1
)