Một số tính chất của hệ thống kết hợp xung ẩn qua phép toán phân thời lượng φ-Hilfer

Abdeljawad, T.: Fractional operators with generalized Mittag-Leffler kernels and their iterated differintegrals. Chaos 29, 023102 (2019) https://doi.org/10.1063/1.5085726 Abdeljawad, T.: Fractional difference operators with discrete generalized Mittag-Leffler kernels. Chaos Solitons Fractals 126, 315–324 (2019) Abdeljawad, T., Baleanu, D.: On fractional derivatives with generalized Mittag-Leffler kernels. Adv. Differ. Equ. 2018, 468 (2018) Abdo, M.S., Abdeljawad, T., Ali, S.M., Shah, K., Jarad, F.: Existence of positive solutions for weighted fractional order differential equations. Chaos Solitons Fractals 141, 110341 (2020) Abdo, M.S., Abdeljawad, T., Shah, K., Jarad, F.: Study of impulsive problems under Mittag-Leffler power law. Heliyon 6(10), e05109 (2020) Abdo, M.S., Shah, K., Panchal, S.K., Wahash, H.A.: Existence and Ulam stability results of a coupled system for terminal value problems involving ψ-Hilfer fractional operator. Adv. Differ. Equ. 2020(1), 316 (2020) Abdo, M.S., Thabet, S.T.M., Ahmad, B.: The existence and Ulam–Hyers stability results for ψ-Hilfer fractional integrodifferential equations. J. Pseudo-Differ. Oper. Appl. 11, 1757–1780 (2020). https://doi.org/10.1007/s11868-020-00355-x Agarwal, R.P., Benchohra, M., Hamani, S.: A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions. Acta Appl. Math. 109(3), 973–1033 (2010) Ahmad, B., Alghanmi, M., Nieto, J.J., Alsaedi, A.: On impulsive nonlocal integro-initial value problems involving multi-order Caputo-type generalized fractional derivatives and generalized fractional integrals. Adv. Differ. Equ. 2019(1), 247 (2019) Ahmad, M., Zada, A., Wang, X.: Existence, Uniqueness and Stability of Implicit Switched Coupled Fractional Differential Equations of ψ-Hilfer Type. Int. J. Nonlinear Sci. Numer. Simul. 1(ahead–of–print) (2020) Al-Mayyahi, S.Y., Abdo, M.S., Redhwan, S.S., Abood, B.N.: Boundary value problems for a coupled system of Hadamard-type fractional differential equations. IAENG Int. J. Appl. Math. 51(1), 1–10 (2021) Ali, A., Shah, K., Jarad, F.: Ulam–Hyers stability analysis to a class of nonlinear implicit impulsive fractional differential equations with three point boundary conditions. Adv. Differ. Equ. 2019(1), 7 (2019) Ali, A., Shah, K., Jarad, F., et al.: Existence and stability analysis to a coupled system of implicit type impulsive boundary value problems of fractional-order differential equations. Adv. Differ. Equ. 2019, 101 (2019). https://doi.org/10.1186/s13662-019-2047-y Aljaaidi, T.A., Pachpatte, D.B.: The Minkowski’s inequalities via ψ-Riemann–Liouville fractional integral operators. Rend. Circ. Mat. Palermo (2) Suppl. (2020). https://doi.org/10.1007/s12215-020-00539-w Almalahi, M.A., Abdo, M.S., Panchal, S.K.: On the theory of fractional terminal value problem with ψ-Hilfer fractional derivative. AIMS Math. 5(5), 4889 (2020). https://doi.org/10.3934/math.2020312 Almalahi, M.A., Abdo, M.S., Panchal, S.K.: Existence and Ulam–Hyers stability results of a coupled system of ψ-Hilfer sequential fractional differential equations. Results Appl. Math. 10, 100142 (2021). https://doi.org/10.1016/j.rinam.2021.100142 Almalahi, M.A., Abdo, M.S., Panchal, S.K.: Existence and Ulam–Hyers–Mittag-Leffler stability results of ψ-Hilfer nonlocal Cauchy problem. Rend. Circ. Mat. Palermo (2) Suppl. 70, 57–77 (2021). https://doi.org/10.1007/s12215-020-00484-8 Almalahi, M.A., Panchal, S.K.: On the theory of ψ-Hilfer nonlocal Cauchy problem. J. Sib. Fed. Univ. Math. Phys. 14(2), 159–175 (2021). https://doi.org/10.17516/1997-1397-2021-14-2-161-177 Almalahi, M.A., Panchal, S.K., Jarad, F.: Stability results of positive solutions for a system of ψ-Hilfer fractional differential equations. Chaos Solitons Fractals 147, 110931 (2021). https://doi.org/10.1016/j.chaos.2021.110931 Almalahi, M.A., Panchal, S.K., Jarad, F., Abdeljawad, T.: Ulam–Hyers–Mittag-Leffler stability for tripled system of weighted fractional operator with TIME delay. Adv. Differ. Equ. 2021, 299 (2021). https://doi.org/10.1186/s13662-021-03455-0 Almeida, R.: A Caputo fractional derivative of a function with respect to another function. Commun. Nonlinear Sci. Numer. Simul. 44, 460–481 (2017) Almeida, R., Malinowska, A.B., Odzijewicz, T.: Fractional differential equations with dependence on the Caputo–Katugampola derivative. J. Comput. Nonlinear Dyn. 11(6) (2016). https://doi.org/10.1115/1.4034432 Alsulami, H.H., Ntouyas, S.K., Agarwal, R.P., Ahmad, B., Alsaedi, A.: A study of fractional-order coupled systems with a new concept of coupled non-separated boundary conditions. Bound. Value Probl. 2017, 68 (2017) Atangana, A.: Fractal-fractional differentiation and integration: connecting fractal calculus and fractional calculus to predict complex system. Chaos Solitons Fractals 102, 396–406 (2017) Atangana, A., Baleanu, D.: New fractional derivative with non-local and non-singular kernel. Therm. Sci. 20(2), 757–763 (2016) Atangana, A., Baleanu, D.: New fractional derivatives with non-local and non-singular kernel: theory and application to heat transfer model. Therm. Sci. 20(2), 763–769 (2016) Benchohra, M., Seba, D.: Impulsive fractional differential equations in Banach spaces. Electron. J. Qual. Theory Differ. Equ. 8(1), 14 (2009) Benchohra, M., Slimani, B.A.: Existence and uniqueness of solutions to impulsive fractional differential equations. Electron. J. Differ. Equ. 2009, 10 (2009) Deimling, K.: Nonlinear Functional Analysis. Springer, New York (1985) Derbazi, C., Baitiche, Z., Abdo, M.S., Abdeljawad, T.: Qualitative analysis of fractional relaxation equation and coupled system with ψ-Caputo fractional derivative in Banach spaces. AIMS Math. 6(3), 2486–2509 (2021) Granas, A., Dugundji, J.: Fixed Point Theory. Springer, Berlin (2013) Guo, T.L.: Nonlinear impulsive fractional differential equations in Banach spaces. Topol. Methods Nonlinear Anal. 42(1), 221–232 (2013) Jarad, F., Abdeljawad, T.: Generalized fractional derivatives and Laplace transform. Discrete Contin. Dyn. Syst., Ser. S 2019, 709 (2019) Jarad, F., Abdeljawad, T., Baleanu, D.: Caputo-type modification of the Hadamard fractional derivatives. Adv. Differ. Equ. 2012(1), 142 (2012) Kharade, J.P., Kishor, D.K.: On the impulsive implicit ψ-Hilfer fractional differential equations with delay. Math. Methods Appl. Sci. 43(4), 1938–1952 (2020) Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam (2006) Oliveira, E., Sousa, J.V.C.: Ulam–Hyers–Rassias stability for a class of fractional integro-differential equations. Results Math. 73(3), 111 (2018) Podlubny, I.: Fractional Differential Equations. Academic Press, New York (1999) Rus, I.A.: Ulam stabilities of ordinary differential equations in a Banach space. Carpath. J. Math. 26, 103–107 (2010) Samko, S.G., Kilbas, A.A., Marichev, O.I.: Fractional Integrals and Derivatives. Gordon & Breach, Yverdon (1993) Sousa, J.V.C., de Oliveira, C.E.: On the ψ-Hilfer fractional derivative. Commun. Nonlinear Sci. Numer. Simul. 60, 72–91 (2018) Sousa, J.V.C., de Oliveira, C.E.: On the Ulam–Hyers–Rassias stability for nonlinear fractional differential equations using the ψ-Hilfer operator. J. Fixed Point Theory Appl. 20(3), 96 (2018) Sousa, J.V.C., de Oliveira, C.E.: A Gronwall inequality and the Cauchy-type problem by means of ψ-Hilfer operator. Differ. Equ. Appl. 11(1), 87–106 (2019) Wang, J., Feckan, M., Zhou, Y.: A survey on impulsive fractional differential equations. Fract. Calc. Appl. Anal. 19(4), 806–831 (2016)