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Pure Mathematics

Analysis of Caputo-Hadamard fractional neutral delay differential equations involving Hadamard integral and unbounded delays: Existence and uniqueness

, ORCID Icon & | (Reviewing editor:)
Article: 2321669 | Received 27 Dec 2023, Accepted 16 Feb 2024, Published online: 29 Feb 2024

References

  • Abuasbeh, K., Awadalla, M., & Jneid, M. (2021). Nonlinear hadamard fractional boundary value problems with different orders. Rocky Mountain Journal of Mathematics, 51(1). https://doi.org/10.1216/rmj.2021.51.17
  • Aissani, K., & Benchohra, M. (2013). Impulsive fractional differential inclusions with infinite delay. Electronic Journal of Differential Equations, 2013(42), 1–21. https://doi.org/10.14232/ejqtde.2013.1.42
  • Almeida, R., Malinowska, A. B., & Odzijewicz, T. (2018). An extension of the fractional gronwall inequality. In Conference on Non-Integer Order Calculus and Its Applications, Springer. pp. 20–28.
  • Aphithana, A., Ntouyas, S. K., & Tariboon, J. (2015). Existence and uniqueness of symmetric solutions for fractional differential equations with multi-order fractional integral conditions. Boundary Value Problems, 2015(1), 1–14. https://doi.org/10.1186/s13661-015-0329-1
  • Arab, M., Awadalla, M., Manigandan, M., Abuasbeh, K., Mahmudov, N. I., & Nandha Gopal, T. (2023). On the existence results for a mixed hybrid fractional differential equations of sequential type. Fractal and Fractional, 7(3), 229. https://doi.org/10.3390/fractalfract7030229
  • Atay, F. M. (2003). Distributed delays facilitate amplitude death of coupled oscillators. Physical Review Letters, 91(9), 094101. https://doi.org/10.1103/PhysRevLett.91.094101
  • Awadalla, M., Hannabou, M., Abuasbeh, K., & Hilal, K. (2023). A novel implementation of dhage’s fixed point theorem to nonlinear sequential hybrid fractional differential equation. Fractal and Fractional, 7(2), 144. https://doi.org/10.3390/fractalfract7020144
  • Awadalla, M., Subramanian, M., Manigandan, M., & Abuasbeh, K. (2022). Existence and hu stability of solution for coupled system of fractional-order with integral conditions involving caputo-hadamard derivatives, hadamard integrals. Journal of Function Spaces, 2022, 1–11. https://doi.org/10.1155/2022/9471590
  • Awadalla, M., Yameni, Y., & Abuassba, K. (2019). A new fractional model for the cancer treatment by radiotherapy using the hadamard fractional derivative. Online Math, 1(2), 14–18. https://doi.org/10.5281/Zenodo.3046037
  • Baculíková, B., & Džurina, J. (2011). Oscillation theorems for second-order nonlinear neutral differential equations. Computers & Mathematics with Applications, 62(12), 4472–4478. https://doi.org/10.1016/j.camwa.2011.10.024
  • Baker, C., Bocharov, G., Paul, C., & Rihan, F. (1998). Modelling and analysis of time-lags in some basic patterns of cell proliferation. Journal of Mathematical Biology, 37(4), 341–371. https://doi.org/10.1007/s002850050133
  • Benchohra, M., Henderson, J., Ntouyas, S., & Ouahab, A. (2008). Existence results for fractional order functional differential equations with infinite delay. Journal of Mathematical Analysis and Applications, 338(2), 1340–1350. https://doi.org/10.1016/j.jmaa.2007.06.021
  • Bocharov, G. A., & Rihan, F. A. (2000). Numerical modelling in biosciences using delay differential equations. Journal of Computational and Applied Mathematics, 125(1–2), 183–199. https://doi.org/10.1016/S0377-0427(00)00468-4
  • Boyd, D. W., & Wong, J. S., On nonlinear contractions. Proceedings of the American Mathematical Society 20. (1969), pp. 458–464.
  • Cai, M., Em Karniadakis, G., & Li, C. (2022). Fractional seir model and data-driven predictions of COVID-19 dynamics of omicron variant. Chaos: An Interdisciplinary Journal of Nonlinear Science, 32(7). https://doi.org/10.1063/5.0099450
  • Cai, R., Ge, F., Chen, Y., & Kou, C. (2019). Regional gradient controllability of ultra-slow diffusions involving the hadamard-caputo time fractional derivative. 10(1), 141–156. https://doi.org/10.3934/mcrf.2019033
  • Chang, Y.-K. (2007). Controllability of impulsive functional differential systems with infinite delay in banach spaces. Chaos, Solitons & Fractals, 33(5), 1601–1609. https://doi.org/10.1016/j.chaos.2006.03.006
  • Chang, Y.-K., Anguraj, A., & Arjunan, M. M. (2008). Existence results for impulsive neutral functional differential equations with infinite delay. Nonlinear Analysis: Hybrid Systems, 2(1), 209–218. https://doi.org/10.1016/j.nahs.2007.10.001
  • Culshaw, R. V., Ruan, S., & Webb, G. (2003). A mathematical model of cell-to-cell spread of hiv-1 that includes a time delay. Journal of Mathematical Biology, 46(5), 425–444. https://doi.org/10.1007/s00285-002-0191-5
  • Dabas, J., & Chauhan, A. (2013). Existence and uniqueness of mild solution for an impulsive neutral fractional integro-differential equation with infinite delay. Mathematical and Computer Modelling, 57(3–4), 754–763. https://doi.org/10.1016/j.mcm.2012.09.001
  • Deimling, K. (2010). Nonlinear functional analysis. Courier Corporation.
  • Derbazi, C., & Hammouche, H. (2020). Boundary value problems for caputo fractional differential equations with nonlocal and fractional integral boundary conditions. Arabian Journal of Mathematics, 9(3), 531–544. https://doi.org/10.1007/s40065-020-00288-9
  • Dhaniya, S., Kumar, A., Khan, A., Abdeljawad, T., Alqudah, M. A., & Pandir, Y. (2023). Existence results of langevin equations with caputo–hadamard fractional operator. Journal of Mathematics, 2023, 1–12. https://doi.org/10.1155/2023/2288477
  • Djema, W., Mazenc, F., Bonnet, C., Clairambault, J., & Fridman, E. (2018). Stability analysis of a nonlinear system with infinite distributed delays describing cell dynamics. Proceedings of the 2018 Annual American Control Conference (ACC), US (pp. 1220–1223). IEEE.
  • El-Karamany, A. S., & Ezzat, M. A. (2011). On fractional thermoelasticity. Mathematics and Mechanics of Solids, 16(3), 334–346. https://doi.org/10.1177/1081286510397228
  • Fridman, E. (2014). Introduction to time-delay systems: Analysis and control. Springer.
  • Gambo, Y. Y., Jarad, F., Baleanu, D., & Abdeljawad, T. (2014). On caputo modification of the hadamard fractional derivatives. Advances in Difference Equations, 2014(1), 1–12. https://doi.org/10.1186/1687-1847-2014-10
  • Garra, R., Orsingher, E., & Polito, F. (2018). A note on hadamard fractional differential equations with varying coefficients and their applications in probability. Mathematics, 6(1), 4. https://doi.org/10.3390/math6010004
  • Gopalsamy, K., & He, X.-Z. (1994). Stability in asymmetric hopfield nets with transmission delays. Physica D: Nonlinear Phenomena, 76(4), 344–358. https://doi.org/10.1016/0167-2789(94)90043-4
  • Granas, A., & Dugundji, J. (2003). Fixed point theory (Vol. 14). Springer.
  • Hadamard, J. (1892). Essai sur l’étude des fonctions données par leur développement de taylor. Journal de mathématiques pures et appliquées, 8(1892), 101–186. https://eudmi.org/doc-233965
  • Hale, J. K., & Lunel, S. M. V. (2013). Introduction to functional differential equations (Vol. 99). Springer Science & Business Media.
  • Jarad, F., Abdeljawad, T., & Baleanu, D. (2012). Caputo-type modification of the hadamard fractional derivatives. Advances in Difference Equations, 2012(1), 1–8. https://doi.org/10.1186/1687-1847-2012-142
  • Jessop, R., & Campbell, S. A. (2010). Approximating the stability region of a neural network with a general distribution of delays. Neural Networks, 23(10), 1187–1201. https://doi.org/10.1016/j.neunet.2010.06.009
  • Josić, K., López, J. M., Ott, W., Shiau, L., Bennett, M. R., & Haugh, J. M. (2011). Stochastic delay accelerates signaling in gene networks. PloS Computational Biology, 7(11), e1002264. https://doi.org/10.1371/journal.pcbi.1002264
  • Kilbas, A. (2006). Theory and applications of fractional differential equations.
  • Kuang, Y., & Smith, H. (1993). Global stability for infinite delay lotka-volterra type systems. Journal of Differential Equations, 103(2), 221–246. https://doi.org/10.1006/jdeq.1993.1048
  • Kyrychko, Y., & Hogan, S. (2010). On the use of delay equations in engineering applications. Journal of Vibration and Control, 16(7–8), 943–960. https://doi.org/10.1177/1077546309341100
  • Lakshmanan, S., Rihan, F. A., Rakkiyappan, R., & Park, J. H. (2014). Stability analysis of the differential genetic regulatory networks model with time-varying delays and markovian jumping parameters. Nonlinear Analysis: Hybrid Systems, 14, 1–15. https://doi.org/10.1016/j.nahs.2014.04.003
  • Liu, Y. (2003). Boundary value problems on half-line for functional differential equations with infinite delay in a banach space. Nonlinear Analysis: Theory, Methods & Applications, 52(7), 1695–1708. https://doi.org/10.1016/S0362-546X(02)00283-3
  • Li, S., & Zhang, S. (2020). Existence of solutions for fractional evolution equations with infinite delay and almost sectorial operator. Mathematical Problems in Engineering, 2020, 1–10. https://doi.org/10.1155/2020/6614920
  • Mainardi, F. (2012). Some basic problem in continuum and statistical mechanics.
  • Mesloub, S., & Gadain, H. E. (2020). A priori bounds of the solution of a one point ibvp for a singular fractional evolution equation. Advances in Difference Equations, 2020(1), 1–12. https://doi.org/10.1186/s13662-020-03049-2
  • Michiels, W., Morărescu, C.-I., & Niculescu, S.-I. (2009). Consensus problems with distributed delays, with application to traffic flow models. SIAM Journal on Control and Optimization, 48(1), 77–101. https://doi.org/10.1137/060671425
  • Moaaz, O., Chatzarakis, G., & Muhib, A. (2020). Neutral delay differential equations: An improved approach and its applications in the oscillation theory. Authorea Preprints. https://doi.org/10.22541/au.159835154.40305175
  • Norouzi, F., & N’guérékata, G. M. (2021). Existence results to a ψ-hilfer neutral fractional evolution equation with infinite delay. Nonautonomous Dynamical Systems, 8(1), 101–124. https://doi.org/10.1515/msds-2020-0128
  • Rakkiyappan, R., Velmurugan, G., Rihan, F. A., & Lakshmanan, S. (2016). Stability analysis of memristor-based complex-valued recurrent neural networks with time delays. Complexity, 21(4), 14–39. https://doi.org/10.1002/cplx.21618
  • Rezapour, S., Ntouyas, S. K., Amara, A., Etemad, S., & Tariboon, J. (2021). Some existence and dependence criteria of solutions to a fractional integro-differential boundary value problem via the generalized gronwall inequality. Mathematics, 9(11), 1165. https://doi.org/10.3390/math9111165
  • Rihan, F. A. (2021). Delay differential equations and applications to biology. Springer.
  • Roesch, O., & Roth, H. (2005). Remote control of mechatronic systems over communication networks. Proceedings of the IEEE International Conference Mechatronics and Automation, 2005, Niagara, falls, Canada (Vol.3, pp. 1648–1653). IEEE.
  • Saeed, U. (2023). A method for solving caputo–hadamard fractional initial and boundary value problems. Mathematical Methods in the Applied Sciences, 46(13), 13907–13921. https://doi.org/10.1002/mma.9297
  • Sipahi, R., Atay, F. M., & Niculescu, S.-I. (2008). Stability of traffic flow behavior with distributed delays modeling the memory effects of the drivers. SIAM Journal on Applied Mathematics, 68(3), 738–759. https://doi.org/10.1137/060673813
  • Tariboon, J., Ntouyas, S. K., Thaiprayoon, C. (2014). Nonlinear langevin equation of hadamard-caputo type fractional derivatives with nonlocal fractional integral conditions. Advances in Mathematical Physics, 2014, 1–15. https://doi.org/10.1155/2014/372749
  • Tunc, C., & Bazighifan, O. (2019). Some new oscillation criteria for fourth-order neutral differential equations with distributed delay. Electronic Journal of Mathematical Analysis and Applications, 7(1), 235–241. https://fcag-Egypt.com/Journal/EGMAA
  • Yan, B. (2001). Boundary value problems on the half-line with impulses and infinite delay. Journal of Mathematical Analysis and Applications, 259(1), 94–114. https://doi.org/10.1006/jmaa.2000.7392
  • Yin, C.-Y., Liu, F., & Anh, V. (2007). Numerical simulation of the nonlinear fractional dynamical systems with fractional damping for the extensible and inextensible pendulum. Journal of Algorithms & Computational Technology, 1(4), 427–447. https://doi.org/10.1260/174830107783133888
  • Zhao, K., & Ma, Y. (2021). Study on the existence of solutions for a class of nonlinear neutral hadamard-type fractional integro-differential equation with infinite delay. Fractal and Fractional, 5(2), 52. https://doi.org/10.3390/fractalfract5020052