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Kết quả tồn tại cho các phương trình vi phân chức năng trung tính phân số với độ trễ vô hạn và điều kiện biên không đặc trưng
Tóm tắt
Trong bài báo này, chúng tôi thiết lập các tiêu chí đủ để đảm bảo sự tồn tại của các nghiệm và tính duy nhất cho một lớp các phương trình vi phân phân số trung tính kiểu Caputo bổ sung với độ trễ vô hạn và các điều kiện biên không địa phương có liên quan đến các đạo hàm phân số. Lý thuyết về độ trễ vô hạn và các định lý điểm cố định chuẩn được áp dụng để thu được các kết quả tồn tại cho bài toán đã cho. Các ví dụ sẽ được xây dựng để minh họa các kết quả đạt được.
Từ khóa
Tài liệu tham khảo
Kuang, Y.: Delay Differential Equations with Applications in Population Dynamics. Mathematics in Science and Engineering, vol. 191. Academic Press, Boston (1993)
Burić, N., Todorović, D.: Dynamics of delay-differential equations modelling immunology of tumor growth. Chaos Solitons Fractals 13(4), 645–655 (2002)
Carvalho, A., Pinto, C.M.A.: A delay fractional order model for the co-infection of malaria and HIV/AIDS. Int. J. Dyn. Control 5(1), 168–186 (2017)
Pati, S., Graef, J.R., Padhi, S.: Positive periodic solutions to a system of nonlinear differential equations with applications to Lotka-Volterra-type ecological models with discrete and distributed delays. J. Fixed Point Theory Appl. 21(3), 80 (2019)
Bennett, D.: Applications of Delay Differential Equations in Physiology and Epidemiology. Thesis (Ph. D.), University of Surrey (United Kingdom). ProQuest LLC, Ann Arbor, MI (2005)
Rajavel, S., Samidurai, R., Cao, J., Alsaedi, A., Ahmad, B.: Finite-time non-fragile passivity control for neural networks with time-varying delay. Appl. Math. Comput. 297(15), 145–158 (2017)
Xu, W., Zhu, S., Fang, X., Wang, W.: Adaptive anti-synchronization of memristor-based complex-valued neural networks with time delays. Physica A 535, 122427 (2019)
Li, R., Cao, J., Alsaedi, A., Ahmad, B.: Passivity analysis of delayed reaction-diffusion Cohen-Grossberg neural networks via Hardy-Poincaré inequality. J. Franklin Inst. 354(7), 3021–3038 (2017)
Hale, J.K., Kato, J.: Phase space for retarded equations with infinite delay. Funkc. Ekvacioj 21(1), 11–41 (1978)
Kappel, F., Schappacher, W.: Some considerations to the fundamental theory of infinite delay equations. J. Differ. Equ. 37(2), 141–183 (1980)
Schumacher, K.: Existence and continuous dependence for functional-differential equations with unbounded delay. Arch. Ration. Mech. Anal. 67(4), 315–335 (1978)
Corduneanu, C., Lakshmikantham, V.: Equations with unbounded delay: a survey. Nonlinear Anal. 4(5), 831–877 (1980)
Hino, Y., Murakami, S., Naito, T.: Functional-Differential Equations with Infinite Delay. Lecture Notes in Mathematics, vol. 1473. Springer, Berlin (1991)
Hale, J.K.: Functional differential equations with infinite delays. J. Math. Anal. Appl. 48, 276–283 (1974)
Lakshmikantham, V., Wen, L.Z., Zhang, B.G.: Theory of Differential Equations with Unbounded Delay. Mathematics and Its Applications, vol. 298. Kluwer Academic, Dordrecht (1994)
Benchohra, M., Henderson, J., Ntouyas, S.K., Ouahab, A.: Existence results for fractional order functional differential equations with infinite delay. J. Math. Anal. Appl. 338, 1340–1350 (2008)
Nouri, K., Nazari, M., Keramati, B.: Existence results of solutions for some fractional neutral functional integro-differential equations with infinite delay (2017) https://doi.org/10.20944/preprints201706.0090.v1
Ahmad, B., Alghanmi, M., Alsaedi, A., Agarwal, R.P.: Nonlinear impulsive multiorder Caputo tgype generalized fractional differential equations with infinite delay. Mathematics 7(11), 1108 (2019)
Chen, C., Dong, O.: Existence and Hyers–Ulam stability for a multi-term fractional differential equation with infinite delay. Mathematics 10(7), 1013 (2022)
Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies, vol. 204. Elsevier, Amsterdam (2006)
Krasnoselskii, M.A.: Two remarks on the method of successive approximations. Usp. Mat. Nauk 10, 123–127 (1955)
Granas, A., Dugundji, J.: Fixed Point Theory. Springer, New York (2003)
Zhou, Y., Jiao, F., Li, J.: Existence and uniqueness for fractional neutral differential equations with infinite delay. Nonlinear Anal. 71(7–8), 3249–3256 (2009)
Agarwal, R.P., Zhou, Y., He, Y.: Existence of fractional neutral functional differential equations. Comput. Math. Appl. 59(3), 1095–1100 (2010)
Chauhan, A., Dabas, J., Kumar, M.: Integral boundary-value problem for impulsive fractional functional differential equations with infinite delay. Electron. J. Differ. Equ. 2012, 229 (2012)
Dabas, J., Chauhan, A.: Existence and uniqueness of mild solution for an impulsive neutral fractional integro-differential equation with infinite delay. Math. Comput. Model. 57(3–4), 754–763 (2013)
Bao, H., Cao, J.: Existence of solutions for fractional stochastic impulsive neutral functional differential equations with infinite delay. Adv. Differ. Equ. 2017, 66 (2017)
Zhao, K., Ma, Y.: Study on the existence of solutions for a class of nonlinear neutral Hadamard-type fractional integro-differential equation with infinite delay. Fractal Fract. 5(2), 52 (2021)