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Stability and Numerical Analysis of a Coupled System of Piecewise Atangana–Baleanu Fractional Differential Equations with Delays

  • Mohammed A. Almalahi [2] ; K. A. Aldwoah [1] ; Kamal Shah [3] ; Thabet Abdeljawad [4]
    1. [1] Islamic University of Madinah

      Islamic University of Madinah

      Arabia Saudí

    2. [2] Hajjah University
    3. [3] Prince Sultan University & University of Malakand
    4. [4] Prince Sultan University, China Medical University, Sefako Makgatho Health Sciences University, Kyung Hee University
    Mostrar afiliaciones +
  • Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 3, 2024
  • Idioma: inglés
  • Enlaces
  • Resumen

    • This paper focuses on using piecewise derivatives to simulate the dynamic behavior and investigate the crossover effect within the coupled fractional system with delays by dividing the study interval into two subintervals. We establish and prove significant lemmas concerning piecewise derivatives. Furthermore, we extend and develop the necessary conditions for the existence and uniqueness of solutions, while also investigating the Hyers–Ulam stability results of the proposed system. The results are derived using the Banach contraction principle and the Leary–Schauder alternative fixed-point theorem. Additionally, we employ a numerical method based on Newton’s interpolation polynomials to compute approximate solutions for the considered system. Finally, we provide an illustrative example demonstrating our theoretical conclusions’ practical application

  • Referencias bibliográficas
    • 1. Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego (1999)
    • 2. Samko, S.G., Kilbas, A.A., Marichev, O.I.: Fractional Integrals and Derivatives: Theory and Applications. Gordon & Breach, Yverdon...
    • 3. Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. North-Holland Mathematics...
    • 4. Caputo, M., Fabrizio, M.: A new definition of fractional derivative without singular kernel. Prog. Fract. Differ. Appl. 1(2), 73–85 (2015)
    • 5. Atangana, A., Baleanu, D.: New fractional derivative with non-local and non-singular kernel. Therm. Sci. 20(2), 757–763 (2016)
    • 6. Djennadi, S., Shawagfeh, N., Arqub, O.A.: Well-posedness of the inverse problem of time fractional heat equation in the sense of the Atangana–Baleanu...
    • 7. Heydari, M.H., Razzaghi, M.: A numerical approach for a class of nonlinear optimal control problems with piecewise fractional derivative....
    • 8. Khan, H., Alzabut, J., Shah, A., He, Z. Y., Etemad, S., Rezapour, S., Zada, A.: On fractal-fractional waterborne disease model: a study...
    • 9. Hussain, S.,Madi, E.N., Khan, H., Gulzar, H., Etemad, S., Rezapour, S., Kaabar,M.K.: On the stochastic modeling of COVID-19 under the environmental...
    • 10. Kumar, S., Chauhan, R.P., Momani, S., Hadid, S.: Numerical investigations on COVID-19 model through singular and non-singular fractional...
    • 11. Khan, A., Gómez-Aguilar, J.F., Khan, T.S., Khan, H.: Stability analysis and numerical solutions of fractional order HIV/AIDS model. Chaos...
    • 12. Begum, R., Tunç, O., Khan, H., Gulzar, H., Khan, A.: A fractional order Zika virus model with Mittag– Leffler kernel. Chaos Solitons Fractals...
    • 13. Ghanbari, B.: On approximate solutions for a fractional prey-predator model involving the Atangana– Baleanu derivative. Adv. Differ. Equ....
    • 14. Ghanbari, B.: A new model for investigating the transmission of infectious diseases in a prey–predator system using a non-singular fractional...
    • 15. Ghanbari, B.: Chaotic behaviors of the prevalence of an infectious disease in a prey and predator system using fractional derivatives....
    • 16. Ghanbari, B.: On the modeling of the interaction between tumor growth and the immune system using some new fractional and fractional-fractal...
    • 17. Ghanbari, B.: A fractional system of delay differential equation with nonsingular kernels in modeling hand-foot-mouth disease. Adv. Differ....
    • 18. Maayah, B., Arqub, O.A., Alnabulsi, S., Alsulami, H.: Numerical solutions and geometric attractors of a fractional model of the cancer-immune...
    • 19. Abu Arqub, O., Singh, J., Alhodaly, M.: Adaptation of kernel functions-based approach with Atangana– Baleanu–Caputo distributed order...
    • 20. Almalahi, M.A., Ibrahim, A.B., Almutairi, A., Bazighifan, O., Aljaaidi, T.A., Awrejcewicz, J.: A qualitative study on second-order nonlinear...
    • 21. Almalahi, M.A., Panchal, S.K.: Some properties of implicit impulsive coupled system via ϕ-Hilfer fractional operator. Bound. Value Probl....
    • 22. Almalahi, M.A., Ghanim, F., Botmart, T., Bazighifan, O., Askar, S.: Qualitative analysis of Langevin integro-fractional differential equation...
    • 23. Almeida, R.: A Caputo fractional derivative of a function with respect to another function. Commun. Nonlinear Sci. Numer. Simul. 44, 460–481...
    • 24. Jarad, F., Abdeljawad, T., Hammouch, Z.: On a class of ordinary differential equations in the frame of Atangana–Baleanu fractional derivative....
    • 25. Ahmad, B., Ntouyas, S.K.: Existence results for a coupled system of Caputo type sequential fractional differential equations with nonlocal...
    • 26. Atangana, A., Araz, S.˙I: New concept in calculus: piecewise differential and integral operators. Chaos Solitons Fractals 145, 110638...
    • 27. Zeb, A., Atangana, A., Khan, Z.A., Djillali, S.: A robust study of a piecewise fractional order COVID-19 mathematical model. Alex. Eng....
    • 28. Zhao, Y., Elattar, E.E., Khan, M.A., Asiri, M., Sunthrayuth, P.: The dynamics of the HIV/AIDS infection in the framework of piecewise...
    • 29. Ahmad, S., Yassen, M.F., Alam, M.M., Alkhati, S., Jarad, F., Riaz, M.B.: A numerical study of dengue internal transmission model with...
    • 30. Shah, K., Naz, H., Abdeljawad, T., Abdalla, B.: Study of fractional order dynamical system of viral infection disease under piecewise...
    • 31. Atangana, A., Araz, S.˙I: Modeling third waves of Covid-19 spread with piecewise differential and integral operators: Turkey, Spain and...
    • 32. Almalahi,M.A., Panchal, S.K., Jarad, F., Abdo,M.S., Shah, K., Abdeljawad, T.: Qualitative analysis of a fuzzy Volterra–Fredholm integrodifferential...
    • 33. Aldwoah, K.A., Almalahi, M.A., Shah, K.: Theoretical and numerical simulations on the hepatitis B virus model through a piecewise fractional...
    • 34. Thabet, S.T., Abdo, M.S., Shah, K., Abdeljawad, T.: Study of transmission dynamics of COVID-19 mathematical model under ABC fractional...
    • 35. Arık, ˙IA., Araz, S.˙I: Crossover behaviors via piecewise concept: a model of tumor growth and its response to radiotherapy. Results Phys....
    • 36. Shah, K., Abdeljawad, T., Ali, A.: Mathematical analysis of the Cauchy type dynamical system under piecewise equations with Caputo fractional...
    • 37. Patanarapeelert, N., Asma, A., Ali, A., Shah, K., Abdeljawad, T., Sitthiwirattham, T.: Study of a coupled system with anti-periodic boundary...
    • 38. Ali, A., Ansari, K.J., Alrabaiah, H., Aloqaily, A., Mlaiki, N.: Coupled system of fractional impulsive problem involving power-law kernel...
    • 39. Abdo, M.S., Shammakh, W., Alzumi, H.Z., Alghamd, N., Albalwi, M.D.: Nonlinear piecewise Caputo fractional pantograph system with respect...
    • 40. Alzabut, J.O., Abdeljawad, T.: On existence of a globally attractive periodic solution of impulsive delay logarithmic population model....
    • 41. Saker, S.H., Alzabut, J.O.: On the impulsive delay hematopoiesis model with periodic coefficients. Rocky Mt. J. Math. 39(5), 1657–1688...
    • 42. Zada, A., Waheed, H., Alzabut, J., Wang, X.: Existence and stability of impulsive coupled system of fractional integrodifferential equations....
    • 43. Srinivasa, K., Mundewadi, R.A.: Wavelets approach for the solution of nonlinear variable delay differential equations. Int. J. Math. Comput....
    • 44. Bas, E., Karaoglan, M.: Representation of solution the M-Sturm–Liouville problem with natural transform. Int. J. Math. Comput. Eng. 1(2),...
    • 45. Khan, H., Alzabut, J., Baleanu, D., Alobaidi, G., Rehman, M.U.: Existence of solutions and a numerical scheme for a generalized hybrid...
    • 46. Baleanu, D., Jafari, H., Khan, H., Johnston, S.J.: Results for mild solution of fractional coupled hybrid boundary value problems. Open...
    • 47. Shah, A., Khan, R.A., Khan, A., Khan, H., Gómez-Aguilar, J.F.: Investigation of a system of nonlinear fractional order hybrid differential...
    • 48. Granas, A., Dugundji, J.: Fixed Point Theory. Springer, New York (2003)
    • 49. Banach, S.: Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales. Fund. Math. 3(1), 133–181 (1922)
    • 50. Ulam, S.M.: A Collection of Mathematical Problems. Interscience Publishers, Geneva (1940)
    • 51. Rassias, T.M.: On the stability of the linear mapping in Banach spaces. Proc. Am. Math. Soc. 122(3), 733–736 (1994)
    • 52. Alkahtani, B.S.T., Atangana, A., Koca, I.: Novel analysis of the fractional Zika model using the Adams type predictor-corrector rule for...
    • 53. Garrappa, R.: Numerical solution of fractional differential equations: a survey and a software tutorial. Mathematics 6(2), 16 (2018)
    • 54. Zabidi, N.A., Abdul Majid, Z., Kilicman, A., Rabiei, F.: Numerical solutions of fractional differential equations by using fractional...
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