Ir al contenido

Documat

Analyzing Single and Multi-valued Nonlinear Caputo Two-Term Fractional Differential Equation With Integral Boundary Conditions

  • Ramesh Kumar Vats [1] ; Kanika Dhawan [1] ; V. Vijayakumar [2]
    1. [1] National Institute Of Technology

      National Institute Of Technology

      Japón

    2. [2] Vellore Institute of Technology
  • Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 4, 2024
  • Idioma: inglés
  • Enlaces
  • Resumen

    • This article primarily focuses on the single-valued and multi-valued cases of the class of nonlinear Caputo two-term fractional differential equation with three-point integral boundary conditions. In the single-valued case, we employ Schaefer’s fixed point theorem and the Banach fixed point theorem to establish results regarding the existence and uniqueness of solutions, using linear growth and Lipschitz conditions. Furthermore, we delve into the stability analysis of the single-valued problem using Ulam–Hyers and Ulam–Hyers–Rassias stabilities. In addition to the above, we address the multivalued scenario and provide results on the existence of solutions. This is achieved by employing the Covitz–Nadler FPT and the nonlinear alternative for contractive maps.

      As an application of our fundamental findings, we present illustrative examples that validate our results. These examples have been implemented using MATLAB.

  • Referencias bibliográficas
    • 1. Ahmad, B., Alsaedi, A., Ntouyas, S.K.: Multi-term fractional boundary value problems with four point boundary conditions. J. Nonlinear...
    • 2. Ahmad, B., Ntouyas, S.K., Zhou, Y., Alsaedi, A.: A study of fractional differential equations and inclusions with nonlocal Erdélyi–Kober...
    • 3. Ahmad, M., Zada, A., Ghaderi, M., George, R., Rezapour, S.: On the existence and stability of a neutral stochastic fractional differential...
    • 4. Bagley, R.L., Torvik, P.J.: On the appearance of the fractional derivative in the behavior of real materials. J. Appl. Mech. 51, 294–298...
    • 5. Baleanu, D., Etemad, S., Mohammadi, H., Rezapour, S.: A novel modeling of boundary value problems on the glucose graph. Commun. Nonlinear...
    • 6. Baleanu, D., Jajarmi, A., Mohammadi, H., Rezapour, S.: A new study on the mathematical modelling of human liver with Caputo–Fabrizio fractional...
    • 7. 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...
    • 8. Bedi, P., Kumar, A., Abdeljawad, T., Khan, A.: Existence and approximate controllability of Hilfer fractional evolution equations with...
    • 9. Bedi, P., Kumar, A., Abdeljawad, T., Khan, A.: Existence of mild solutions for impulsive neutral Hilfer fractional evolution equations....
    • 10. Bedi, P., Kumar, A., Khan, A.: Controllability of neutral impulsive fractional differential equations with Atangana–Baleanu–Caputo derivatives....
    • 11. Begum, R., Tunç, O., Khan, H., Gulzar, H., Khan, A.: A fractional order Zika virus model with Mittag–Leffler kernel. Chaos Solitons Fractals...
    • 12. Caponetto, R.: Fractional Order Systems: Modeling and Control Applications. World Scientific, Singapore (2010)
    • 13. Carpentieri, B.: Advances in Dynamical Systems Theory Models, Algorithms and Applications. BoD– Books on Demand, IntechOpen, London-United...
    • 14. Castaing, C., Valadier, M.: Convex Analysis and Measurable Multifunctions. Lecture Notes in Mathematics, vol. 580. Springer, Berlin (1977)
    • 15. Covitz, H., Nadler, S.B., Jr.: Multivalued contraction mappings in generalized metric spaces. Isr. J. Math. 8, 5–11 (1970)
    • 16. Deimling, K.: Multivalued Differential Equations. Walter De Gruyter, Berlin (1992)
    • 17. Devi, A., Kumar, A., Baleanu, D., Khan, A.: On stability analysis and existence of positive solutions for a general non-linear fractional...
    • 18. Devi, A., Kumar, A., Abdeljawad, T., Khan, A.: Stability analysis of solutions and existence theory of fractional Lagevin equation. Alex....
    • 19. Dhawan, K., Vats, R.K., Nain, A.K., Shukla, A.: Well-posedness and Ulam–Hyers stability of Hilfer fractional differential equations of...
    • 20. Dhawan, K., Vats, R.K., Agarwal, R.P.: Qualitative analysis of couple fractional differential equations involving Hilfer Derivative. An....
    • 21. Dhawan, K., Vats, R.K., Kumar, S., Kumar, A.: Existence and Stability analysis for nonlinear boundary value problem involving Caputo fractional...
    • 22. Dhawan, K., Vats, R.K., Vijaykumar, V.: Analysis of neutral fractional differential equation via the method of upper and lower solution....
    • 23. Ehme, J., Eloe, P.W., Henderson, J.: Upper and lower solution methods for fully nonlinear boundary value problems. J. Differ. Equ. 180,...
    • 24. Etemad, S., Avci, I., Kumar, P., Baleanu, D., Rezapour, S.: Some novel mathematical analysis on the fractal-fractional model of the AH1N1/09...
    • 25. Guezane-Lakoud, A., Khaldi, R., Torres, D.F.M.: On a fractional oscillator equation with natural boundary conditions. Prog. Fract. Differ....
    • 26. Hu, Sh., Papageorgiou, N.: Handbook of Multivalued Analysis, vol. I: Theory. Kluwer, Dordrecht (1997)
    • 27. 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...
    • 28. Jeelani, M.B., Saeed, A.M., Abdo, M.S., Shah, K.: Positive solutions for fractional boundary value problems under a generalized fractional...
    • 29. Kamal, S.: Nonlocal boundary value problems for nonlinear toppled system of fractional differential equations. Hacet. J. Math. Stat. 49(1),...
    • 30. Kamenskii, M., Obukhovskii, V., Petrosyan, G., Yao, J.: Boundary value problems for semi-linear differential inclusions of fractional...
    • 31. Kaufmann, E.R., Yao, K.D.: Existence of solutions for a nonlinear fractional order differential equation. Electron. J. Qual. Theory Differ....
    • 32. Khan, H., Alam, K., Gulzar, H., Etemad, S., Rezapour, S.: A case study of fractal–fractional tuberculosis model in China: existence and...
    • 33. Khan, H., Alzabut, J., Baleanu, D., Alobaidi, G., Rehman, M.U.: Existence of solutions and a numerical scheme for a generalized hybrid...
    • 34. Khan, H., Alzabut, J., Gulzar, H., Tunç, O., Pinelas, S.: On system of variable order nonlinear pLaplacian fractional differential equations...
    • 35. Khan, H., Alzabut, J., Shah, A., He, Z.Y., Etemad, S., Rezapour, S., Zada, A.: On fractal–fractional waterborne disease model: a study...
    • 36. Khan, A., Khan, Z.A., Abdeljawad, T., Khan, H.: Analytical analysis of fractional-order sequential hybrid system with numerical application....
    • 37. Khan, A., Li, Y., Shah, K., Khan, T.S.: On coupled-Laplacian fractional differential equations with nonlinear boundary conditions. Complexity...
    • 38. Khan, H., Tunç, C., Khan, A.: Stability results and existence theorems for nonlinear delay-fractional differential equations with ϕ∗ p-operator....
    • 39. Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam (2006)
    • 40. Kisielewicz, M.: Differential Inclusions and Optimal Control. Kluwer, Dordrecht (1991)
    • 41. Lasota, A., Opial, Z.: An application of the Kakutani-Ky Fan theorem in the theory of ordinary differential equations. Bull. Acad. Polon....
    • 42. Mainardi, F.: Fractional Calculus. Springer, Berlin (1997)
    • 43. Matar, M.M., Abbas, M.I., Alzabut, J., Kaabar, M.K., Etemad, S., Rezapour, S.: Investigation of the pLaplacian nonperiodic nonlinear boundary...
    • 44. Mohammadi, H., Kumar, S., Rezapour, S., Etemad, S.: A theoretical study of the Caputo-Fabrizio fractional modeling for hearing loss due...
    • 45. Marazzato, R., Sparavigna, A.C.: Astronomical image processing based on fractional calculus: the astrofractool (2009). arXiv:0910.4637
    • 46. Ntouyas, S.K., Tariboon, J.: Fractional boundary value problems with multiple orders of fractional derivative and integrals. Electron....
    • 47. Oldham, K.B.: Fractional differential equations in electrochemistry. Adv. Eng. Softw. 41, 9–12 (2010)
    • 48. Pales, Z.: Generalized stability of the Cauchy functional equation. Aequationes Math. 56(3), 222–232 (1998)
    • 49. Petryshyn, W.V., Fitzpatrick, P.M.: A degree theory, fixed point theorems, and mapping theorems for multivalued noncompact maps. Trans....
    • 50. Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego (1999)
    • 51. Saeed, A.M., Abdo, M.S., Jeelani, M.B.: Existence and Ulam–Hyers stability of a fractional-order coupled system in the frame of generalized...
    • 52. Shah, K., Abdalla, B., Abdeljawad, T., Gul, R.: Analysis of multipoint impulsive problem of fractionalorder differential equations. Bound....
    • 53. Shah, K., Ali, G., Ansari, K.J., Abdeljawad, T., Meganathan, M., Abdalla, B.: On qualitative analysis of boundary value problem of variable...
    • 54. Szekelyhidi, L.: Ulam’s problem, note on a stability theorem. Can. Math. Bull. 25(4), 500–501 (1982)
    • 55. Tuan, N.H., Mohammadi, H., Rezapour, S.: A mathematical model for COVID-19 transmission by using the Caputo fractional derivative. Chaos...
    • 56. Tabor, J., Tabor, J.: General stability of functional equations of linear type. J. Math. Anal. Appl. 328(1), 192–200 (2007)
    • 57. Telli, B., Souid, M.S., Alzabut, J., Khan, H.: Existence and uniqueness theorems for a variable-order fractional differential equation...
    • 58. Ulam, S.M.: A Collection of the Mathematical Problems. Interscience, New York (1960)
    • 59. Wu, G.C., Baleanu, D., Zeng, S.D.: Discrete chaos in fractional sine and standard maps. Phys. Lett. A 378, 484–87 (2014)
Fundación Dialnet

Mi Documat

Opciones de artículo

Opciones de compartir

Opciones de entorno