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Quasilinear Coupled System in the Frame of Nonsingular ABC-Derivatives with p-Laplacian Operator at Resonance

  • Mokhtar Bouloudene [2] ; Fahd Jarad [1] ; Yassine Adjabi [3] ; Sumati Kumari Panda [4]
    1. [1] China Medical University

      China Medical University

      Taiwán

    2. [2] University of M’hamed Bougara & University of M’hamed Bougara
    3. [3] University of M’hamed Bougara & U.S.T.H.B.
    4. [4] GMR Institute of Technology
    Mostrar afiliaciones +
  • Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 1, 2024
  • Idioma: inglés
  • Enlaces
  • Resumen

    • We investigate the existence of solutions for coupled systems of fractional p-Laplacian quasilinear boundary value problems at resonance given by the Atangana–Baleanu– Caputo (shortly, ABC) derivatives formulations are based on the well-known MittagLeffler kernel utilizing Ge’s application of Mawhin’s continuation theorem. Examples are provided to demonstrate our findings.

  • Referencias bibliográficas
    • 1. Debnath, L.: Recent applications of fractional calculus to science and engineering. Int. J. Math. Math. Sci. 54, 3413–3442 (2003)
    • 2. Angstmann, C.N., Erickson, A.M., Henry, B.I., McGann, A.V., Murray, J.M., Nichols, J.A.: Fractional order compartment models. SIAM J. Appl....
    • 3. Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. Elsevier Science B.V, Amsterdam...
    • 4. Khalil, R., Al, H.M., Yousef, A., Sababheh, M.: A new definition of fractional derivative. J. Comput. Appl. Math. 264, 65–70 (2014)
    • 5. Atangana A., Noutchie S.C.O.: Model of break-bone fever via beta-derivatives. Bio Med. Res. Int. (2014) 2014, Article ID 523159
    • 6. Jarad, F., Baleanu, D., Abdeljawad, A.: Caputo-type modification of the Hadamard fractional derivatives. Adv. Differ. Equ. 142, 2012 (2012)
    • 7. Atangana, A.: On the new fractional derivative and application to nonlinear fisher’s reaction–diffusion equation. Appl. Math. Comput. 273,...
    • 8. Caputo, M., Fabrizio, M.: A new definition of fractional derivative without singular kernel. Prog. Fract. Differ. Appl. 1(2), 1–13 (2015)
    • 9. Atangana, A., Baleanu, D.: New fractional derivatives with nonlocal and non-singular kernel: theory and application to heat transfer model....
    • 10. Losada, J., Nieto, J.J.: Properties of a new fractional derivative without singular kernel. Prog. Fract. Differ. Appl. 2(1), 87–92 (2015)
    • 11. Baleanu, D., Fernandez, A.: On some new properties of fractional derivatives with Mittag-Leffler kernel. Commun. Nonlinear Sci. Numer....
    • 12. Jarad, F., Abdeljawad, T., Hammouch, Z.: On a class of ordinary differential equations in the frame of Atangana–Baleanu fractional derivative....
    • 13. Baleanu, D., Alzabut, J., Jonnalagadda, J.M., Adjabi, Y., Matar, M.M.: A coupled system of generalized Sturm–Liouville problems and Langevin...
    • 14. Ravichandran, C., et al.: On new approach of fractional derivative by Mittag-Leffler kernel to neutral integro-differential systems with...
    • 15. Das, A., Hazarika, B., Panda, S.K., et al.: An existence result for an infinite system of implicit fractional integral equations via generalized...
    • 16. Kumari, P.S., Panthi, D.: Cyclic compatible contraction and related fixed point theorems. Fixed Point Theory Appl 28, 2016 (2016). https://doi.org/10.1186/s13663-016-0521-8
    • 17. Sumati Kumari, P., Alqahtani, O., Karapınar, E.: Some fixed-point theorems in b-dislocated metric space and applications. Symmetry 10,...
    • 18. Panda, S.K., Abdeljawad, T., Ravichandran, C.: Novel fixed point approach to Atangana–Baleanu fractional and Lp-Fredholm integral equations....
    • 19. Panda, S.K., Atangana, A., Abdeljawad, T.: Existence results and numerical study on novel coronavirus 2019-ncov/sars-cov-2 model using...
    • 20. Panda, S.K., Atangana, A., Nieto, J.J.: New insights on novel coronavirus 2019-nCoV/SARS-CoV-2 modelling in the aspect of fractional derivatives...
    • 21. O’Regan, D., Cho, Y.J., Chen, Y.Q.: Topological Degree Theory and Applications. Chapman and Hall/CRC Press, Boca Raton (2006)
    • 22. Mawhin J.: Topological degree methods in nonlinear boundary value problems. In: NSFCBMS Regional Conferences Series in Mathematics. American...
    • 23. Gaines, R.E., Mawhin, J.L.: Coincidence Degree, and Nonlinear Differential Equations, volume 568 of Lecture Notes in Mathematic. Springer...
    • 24. Ge, W., Ren, J.: An extension of Mawhin’s continuation theorem and its application to boundary value problems with a p-Laplacian. Nonlinear...
    • 25. Du, B., Hu, X.: A new continuation theorem for the existence of solutions to p-Laplacian BVP at resonance. Appl. Math. Comput. 208, 172–176...
    • 26. Leibenson, L.S.: General problem of the movement of a compressible fluid in a porous medium. Izv. Akad. Nauk Kirg. SSSR 9, 7–10 (1983)
    • 27. Fulina, S.: On Mawhin’s continuation principles. An. St. Univ. Ovidius Constanta 13(1), 73–78 (2005)
    • 28. Hu, L., Zhang, S., Shl, A.: Existence result for nonlinear fractional differential equation with pLaplacian operator at resonance. J....
    • 29. Lian, L., Ge, W.: The existence of solutions of m-point p-Laplacian boundary value problems at resonance. Acta Math. Appl. Sin. 28, 288–295...
    • 30. Xue, C., Ge, W.: The existence of solutions for multi-point boundary value problem at resonance. Acta Math. Sin. 48, 281–290 (2005)
    • 31. Ma, R.: Existence results of a m-point boundary value problem at resonance. J. Math. Anal. Appl. 294, 147–157 (2004)
    • 32. Lu, S., Ge, W.: On the existence of m-point boundary value problem at resonance for higher order differential equation. J. Math. Anal....
    • 33. Podlubny, I.: Fractional Differential Equations. Academic Press, New York (1999)
    • 34. Miller, K.S., Ross, B.: An Introduction to the Fractional Calculus and Fractional Differential Equations. Wiley, New York (1993)
    • 35. Su, X.: Boundary value problem for a coupled system of nonlinear fractional differential equations. Appl. Math. Lett. 22, 64–69 (2009)
    • 36. Su, X.: Existence of solution of boundary value problem for coupled system of fractional differential equations. Eng. Math. 26, 134–137...
    • 37. Yang, A., Ge, W.: Positive solutions for boundary value problems of N-dimension nonlinear fractional differential system. Bound. Value...
    • 38. Kosmatov, N.: A boundary value problem of fractional order at resonance. Electron. J. Differ. Equ. 135, 1–10 (2010)
    • 39. Jiang, W.: The existence of solutions for boundary value problems of fractional differential equations at resonance. Nonlinear Anal. 74,...
    • 40. Yan, P.: Non-resonance for one-dimensional p-Laplacian with regular restoring. J. Math. Anal. Appl. 285, 141–154 (2003)
    • 41. Ahmad, B., Alsaedi, A.: Existence and uniqueness of solutions for coupled systems of higher-order nonlinear fractional differential equations....
    • 42. Ahmad, B., Nieto, J.J., Alsaedi, A., Aqlan, M.: A coupled system of Caputo-type sequential fractional differential equations with coupled...
    • 43. Agarwal, R.P., Ahmad, B., Garout, D., Alsaedi, A.: Existence results for coupled nonlinear fractional differential equations equipped...
    • 44. Zhou, X., Xu, C.: Well-posedness of a kind of nonlinear coupled system of fractional differential equations. Sci. China Math. 59, 1209–1220...
    • 45. Wang, J., Zhang, Y.: Analysis of fractional order differential coupled systems. Math. Methods Appl. Sci. 38, 3322–3338 (2015)
    • 46. Liu, W., Yan, X., Qi, W.: Positive solutions for coupled nonlinear fractional differential equations. J. Appl. Math., Art. ID 790862 (2014)
    • 47. Hussain, S., et al.: On the stochastic modeling of COVID-19 under the environmental white noise. J. Funct. Spaces 2022, 1–9 (2022)
    • 48. Ahmad, M., et al.: On the existence and stability of a neutral stochastic fractional differential system. Fractal Fract 4, 203 (2022)
    • 49. Mohammadi, H., et al.: A theoretical study of the Caputo–Fabrizio fractional modeling for hearing loss due to Mumps virus with optimal...
    • 50. Khan, H., et al.: A case study of fractal-fractional tuberculosis model in China: existence and stability theories along with numerical...
    • 51. Etemad, S., et al.: Some novel mathematical analysis on the fractal-fractional model of the AH1N1/09 virus and its generalized Caputo-type...
    • 52. Matar, M.M., et al.: Investigation of the p-Laplacian nonperiodic nonlinear boundary value problem via generalized Caputo fractional derivatives....
    • 53. Baleanu, D., et al.: A novel modeling of boundary value problems on the glucose graph. Commun. Nonlinear Sci. Numer. Simul. 100, 105844...
    • 54. Baleanu, D., et al.: A new study on the mathematical modelling of human liver with Caputo–Fabrizio fractional derivative. Chaos, Solitons...
    • 55. Tuan, N.H., Hakimeh, M., Shahram, R.: A mathematical model for COVID-19 transmission by using the Caputo fractional derivative. Chaos,...
    • 56. Baleanu, D., Mohammadi, H., Rezapour, S.: Analysis of the model of HIV-1 infection of C D4+ T-cell with a new approach of fractional...
    • 57. Rehman, M., Khan, R.: A note on boundary value problems for a coupled system of fractional differential equations. Comput. Math. Appl....
    • 58. Jiang, W.: Solvability for a coupled system of fractional differential equations at resonance. Nonlinear Anal. 13, 2285–2292 (2012)
    • 59. Yang, Z., Wang, X., Li, H.: Positive solutions for a system of second-order quasilinear boundary value problems. Nonlinear Anal. 195,...
    • 60. Hu, Z., Liu, W., Liu, J.: Existence of solutions for a coupled system of fractional p-Laplacian equations at resonance. Adv. Difference...
    • 61. Ercan, A., Ozarslan, R., Bas, E.: Existence and uniqueness analysis of solutions for Hilfer fractional spectral problems with applications....
    • 62. Ercan, A.: Comparative analysis for fractional nonlinear Sturm–Liouville equations with singular and non-singular kernels. AIMS Math....
    • 63. Abdeljawad, T., Baleanu, D.: Discrete fractional differences with nonsingular discrete Mittag-Leffler kernels. Adv. Differ. Equ. 2016,...
    • 64. Kuang, J.: Applied Inequalities, p. 132. Shandong Science and Technology Press, Jinan (2014)
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