Analytical analysis of fractional-order sequential hybrid system with numerical application

Deimling, K.: Nonlinear Functional Analysis. Springer, New York (1985) Atangana, A., Araz, S.I.: Mathematical model of Covid-19 spread in Turkey and South Africa: theory, methods and applications. Adv. Differ. Equ. 2020, 659 (2020) Atangana, A., Baleanu, D.: New fractional derivatives with nonlocal and non-singular kernel: theory and application to heat transfer model. Therm. Sci. 20(2), 763–769 (2016) Atangana, A., Araz, S.I.: Nonlinear equations with global differential and integral operators: existence, uniqueness with application to epidemiology. Results Phys. 20, 103593 (2020) Losada, J., Nieto, J.J.: Properties of a new fractional derivative without singular kernel. Prog. Fract. Differ. Appl. 1(2), 87–92 (2015) Caputo, M., Fabrizio, M.: A new definition of fractional derivative without singular kernel. Prog. Fract. Differ. Appl. 1(2), 1–3 (2015) Gorenflo, R., Mainardi, F.: Fractional calculus. In: Fractals and Fractional Calculus in Continuum Mechanics, pp. 223–276. Springer, Vienna (1997) Atangana, A., Owolabi, K.M.: New numerical approach for fractional differential equations. Math. Model. Nat. Phenom. 13(1), 3 (2018) Akgul, A., Modanli, M.: Crank–Nicholson difference method and reproducing kernel function for third order fractional differential equations in the sense of Atangana–Baleanu Caputo derivative. Chaos Solitons Fractals 127, 10–16 (2019) Solis-Perez, J.E., Gomez-Aguilar, J.F., Atangana, A.: Novel numerical method for solving variable-order fractional differential equations with power, exponential and Mittag-Leffler laws. Chaos Solitons Fractals 114, 175–185 (2018) Akinlar, M.A., Tchier, F., Inc, M.: Chaos control and solutions of fractional-order Malkus waterwheel model. Chaos Solitons Fractals 135, 109746 (2020) Khan, H., Gomez-Aguilar, J.F., Khan, A., Khan, T.S.: Stability analysis for fractional order advection–reaction diffusion system. Phys. A, Stat. Mech. Appl. 521, 737–751 (2019) Attia, N., Akgul, A., Seba, D., Nour, A.: An efficient numerical technique for a biological population model of fractional order. Chaos Solitons Fractals 141, 110349 (2020) Atangana, A., Alqahtani, R.T.: New numerical method and application to Keller–Segel model with fractional order derivative. Chaos Solitons Fractals 116, 14–21 (2018) Abdeljawad, T.: On Riemann and Caputo fractional differences. Comput. Math. Appl. 62(3), 1602–1611 (2011) Abdeljawad, T., Fractional, B.D.: Differences and Integration by Parts. J. Comput. Math. 13(3) (2011) Baitiche, Z., Guerbati, K., Benchohra, M., Zhou, Y.: Boundary value problems for hybrid Caputo fractional differential equations. Mathematics 7, 282 (2019) Derbazi, C., Hammouche, H., Benchohra, M., Zhou, Y.: Fractional hybrid differential equations with three-point boundary hybrid conditions. Adv. Differ. Equ. 2019, 125 (2019) Borai, M.M.E., Sayed, W.G.E., Badr, A.A., Tarek, A.: Initial value problem for stochastic hybrid Hadamard fractional differential equation. J. Adv. Math. 16, 8288–8296 (2019) Hilal, K., Kajouni, A.: Boundary value problems for hybrid differential equations with fractional order. Adv. Differ. Equ. 2015, 183 (2015) Ahmad, B., Ntouyas, S.K.: Initial-value problems for hybrid Hadamard fractional differential equations. Electron. J. Differ. Equ. 2014, 161 (2014) Dhage, B.C.: Hybrid fixed point theory in partially ordered normed linear spaces and applications to fractional integral equations. Differ. Equ. Appl. 5, 155184 (2013) Dhage, B.C., Dhage, S.B., Ntouyas, S.K.: Approximating solutions of nonlinear hybrid differential equations. Appl. Math. Lett. 34, 76–80 (2014) Zhang, S.: The existence of a positive solution for a nonlinear fractional differential equation. J. Math. Anal. Appl. 252, 804–812 (2000) Dhage, B.C., Lakshmikantham, V.: Basic results on hybrid differential equations. Nonlinear Anal. Hybrid Syst. 4, 414–424 (2010) Dhage, B.: Quadratic perturbations of periodic boundary value problems of second order ordinary differential equations. Differ. Equ. Appl. 2, 465–486 (2010) Dhage, B.: Periodic boundary value problems of first order Carathéodory and discontinuous differential equations. Nonlinear Funct. Anal. Appl. 13(2), 323–352 (2008) Dhage, B.: Basic results in the theory of hybrid differential equations with mixed perturbations of second type. Funct. Differ. Equ. 19, 1–20 (2012) Herzallah, M.A., Baleanu, D.: On fractional order hybrid differential equations. Abstr. Appl. Anal. 2014, Article ID 389386 (2014) Mahmudov, N., Matar, M.M.: Existence of mild solution for hybrid differential equations with arbitrary fractional order. TWMS J. Pure Appl. Math. 8(2), 160–169 (2017) Jafari, H., Baleanu, D., Khan, H., Khan, R.A., Khan, A.: Existence criterion for the solutions of fractional order p-Laplacian boundary value problems. Bound. Value Probl. 2015, 164 (2015) Ahmad, B., Nieto, J.J.: Existence of solutions for impulsive anti-periodic boundary value problems of fractional order. Taiwan. J. Math. 15(3), 981–993 (2011) Wang, G., Ahmad, B., Zhang, L., Nieto, J.J.: Comments on the concept of existence of solution for impulsive fractional differential equations. Commun. Nonlinear Sci. Numer. Simul. 19(3), 401–403 (2014) Al-Sadi, W., Zhenyou, H., Alkhazzan, A.: Existence and stability of a positive solution for nonlinear hybrid fractional differential equations with singularity. J. Taibah Univ. Sci. 13(1), 951–960 (2019) Khan, R.A., Gul, S., Jarad, F., Khan, H.: Existence results for a general class of sequential hybrid fractional differential equations. Adv. Differ. Equ. 2021(1), 284 (2021) Aljoudi, S., Ahmad, B., Nieto, J.J., Alsaedi, A.: A coupled system of Hadamard type sequential fractional differential equations with coupled strip conditions. Chaos Solitons Fractals 91, 39–46 (2016) Agarwal, P., Baleanu, D., Chen, Y., Momani, S., Machado, J.A.: Fractional calculus. In: Conference Proceedings ICFDA 2018, Amman, Jordan, July 16–18, 2018 (2018) Rajchakit, G., Agarwal, P., Ramalingam, S.: Stability Analysis of Neural Networks (2021) Agarwal, P., Baltaeva, U., Tariboon, J.: Solvability of the boundary-value problem for a third-order linear loaded differential equation with the Caputo fractional derivative. In: Special Functions and Analysis of Differential Equations, pp. 321–334 (2020) Agarwal, P., Dragomir, S.S., Jleli, M., Samet, B. (eds.): Advances in Mathematical Inequalities and Applications Springer, Singapore (2018) Ruzhansky, M., Cho, Y.J., Agarwal, P., Area, I. (eds.): Advances in Real and Complex Analysis with Applications Springer, Singapore (2017) Salahshour, S., Ahmadian, A., Senu, N., Baleanu, D., Agarwal, P.: On analytical solutions of the fractional differential equation with uncertainty: application to the Basset problem. Entropy 17(2), 885–902 (2015) Tariboon, J., Ntouyas, S.K., Agarwal, P.: New concepts of fractional quantum calculus and applications to impulsive fractional q-difference equations. Adv. Differ. Equ. 2015(1), 18 (2015) Morales-Delgado, V.F., Gómez-Aguilar, J.F., Saad, K.M., Khan, M.A., Agarwal, P.: Analytic solution for oxygen diffusion from capillary to tissues involving external force effects: a fractional calculus approach. Phys. A, Stat. Mech. Appl. 523, 48–65 (2019) Thabet, S.T., Etemad, S., Rezapour, S.: On a coupled Caputo conformable system of pantograph problems. Turk. J. Math. 45, 496–519 (2021) Baleanu, D., Etemad, S., Rezapour, S.: On a fractional hybrid integro-differential equation with mixed hybrid integral boundary value conditions by using three operators. Alex. Eng. J. 59(5), 3019–3027 (2020) Baleanu, D., Etemad, S., Rezapour, S.: A hybrid Caputo fractional modeling for thermostat with hybrid boundary value conditions. Bound. Value Probl. 2020(1), 64 (2020) Mohammadi, H., Kumar, S., Rezapour, S., Etemad, S.: A theoretical study of the Caputo–Fabrizio fractional modeling for hearing loss due to Mumps virus with optimal control. Chaos Solitons Fractals 144, 110668 (2021) Matar, M.M., Abbas, M.I., Alzabut, J., Kaabar, M.K., Etemad, S., Rezapour, S.: Investigation of the p-Laplacian nonperiodic nonlinear boundary value problem via generalized Caputo fractional derivatives. Adv. Differ. Equ. 2021(1), 68 (2021) Alizadeh, S., Baleanu, D., Rezapour, S.: Analyzing transient response of the parallel RCL circuit by using the Caputo–Fabrizio fractional derivative. Adv. Differ. Equ. 2020(1), 55 (2020) Baleanu, D., Rezapour, S., Saberpour, Z.: On fractional integro-differential inclusions via the extended fractional Caputo–Fabrizio derivation. Bound. Value Probl.. 2019(1), 79 (2019) Baleanu, D., Etemad, S., Pourrazi, S., Rezapour, S.: On the new fractional hybrid boundary value problems with three-point integral hybrid conditions. Adv. Differ. Equ.. 2019(1), 473 (2019) Aydogan, M.S., Baleanu, D., Mousalou, A., Rezapour, S.: On high order fractional integro-differential equations including the Caputo–Fabrizio derivative. Bound. Value Probl. 2018(1), 90 (2018) Baleanu, D., Mohammadi, H., Rezapour, S.: Analysis of the model of HIV-1 infection of CD4+ CD4+ T-cell with a new approach of fractional derivative. Adv. Differ. Equ. 2020(1), 71 (2020) Caputo, M., Fabrizio, M.: A new definition of fractional derivative without singular kernel. Prog. Fract. Differ. Appl. 1(2), 1–3 (2015) Losada, J., Nieto, J.J.: Properties of a new fractional derivative without singular kernel. Prog. Fract. Differ. Appl. 1(2), 87–92 (2015) Atangana, A., Baleanu, D.: New fractional derivatives with nonlocal and non-singular kernel: theory and application to heat transfer model. Therm. Sci. 20(2), 763–769 (2016) Jarad, F., Abdeljawad, T., Hammouch, Z.: On a class of ordinary differential equations in the frame of Atangana–Baleanu fractional derivative. Chaos Solitons Fractals 117, 16–20 (2018) Alzaid, S.S., Alkahtani, B.S.: Asymptotic analysis of a giving up smoking model with relapse and harmonic mean type incidence rate. Results Phys. 28, 104437 (2021)