Ir al contenido

Documat

Existence and Hyers–Ulam Stability of Jerk-Type Caputo and Hadamard Mixed Fractional Differential Equations

  • Yanli Ma [3] ; Maryam Maryam [1] ; Usman Riaz [2] ; Ioan-Lucian Popa [4] ; Lakhdar Ragoub [5] ; Akbar Zada [1]
    1. [1] University of Peshawar

      University of Peshawar

      Pakistán

    2. [2] Qurtuba University of Science and Information Technology

      Qurtuba University of Science and Information Technology

      Pakistán

    3. [3] Anhui Xinhua University
    4. [4] University of Alba Iulia & Transilvania University of Brasov
    5. [5] University of Prince Mugrin
    Mostrar afiliaciones +
  • Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 3, 2024
  • Idioma: inglés
  • DOI: 10.1007/s12346-024-00971-8
  • Enlaces
  • Resumen

    • This article is concerned with existence of mild solutions for jerk-type fractional differential equations in the sense of Hadamard and Caputo fractional derivatives with separated boundary conditions. For the uniqueness of mild solutions in both cases, Banach contraction principle are followed. Moreover, at least one mild solution of jerktype Caputo–Hadamard and Hadamard–Caputo fractional differential equations can be analyzed using Krasnoselskii’s and Leray–Schauder fixed point theorems. Hyers– Ulam stability and its generalized case for both type of mentioned jerk-type problems can be find out with the help of some conditions and definitions. For the illustration of main results, an example is provided.

  • Referencias bibliográficas
    • 1. Podlubny, I.: Fractional Differential Equations. Elsevier, Amsterdam (1999)
    • 2. Kilbas, A.A., Marichev, O.I., Samko, S.G.: Fractional Integrals and Derivatives (Theory and Applications). Gordon and Breach, Yverdon,...
    • 3. Ahmad, B., Alsaedi, A., Ntouyas, S.K., Tariboon, J.: Hadamard-Type Fractional Differential Equations. Inclusions and Inequalities. Springer,...
    • 4. Diethelm, K.: The Analysis of Fractional Differential Equations: An Application—Oriented Exposition Using Differential Operators of Caputo...
    • 5. Maraaba, T., Baleanu, D., Jarad, F.: Existence and uniqueness theorem for a class of delay differential equations with left and right Caputo...
    • 6. Wei, Z., Li, Q., Che, J.: Initial value problems for fractional differential equations involving Riemann– Liouville sequential fractional...
    • 7. Pooseh, S., Almeida, R., Torres, D.F.: Expansion formulas in terms of integer-order derivatives for the Hadamard fractional integral and...
    • 8. Zada, A., Alam,M., Riaz, U.: Analysis of q-fractional implicit boundary value problems having Stieltjes integral conditions. Math. Meth....
    • 9. Alam, M., Zada, A., Riaz, U.: On a coupled impulsive fractional integrodifferential system with Hadamard derivatives. Qual. Theory Dyn....
    • 10. Miller, K.S., Ross, B.: An Introduction to the Fractional Calculus and Fractional Differential Equations. A Wiley interscience publisher,...
    • 11. Kilbas, A. A., Srivastava, H. M., Trujillo, J. J.: Theory and Applications of the Fractional Differential Equations. North–Holland Mathematics...
    • 12. Zhang, X., Liu, L., Wu, Y.: Multiple positive solutions of a singular fractional differential equation with negatively perturbed term....
    • 13. Zhang, X., Wu, Y., Caccetta, L.: Nonlocal fractional order differential equations with changing-sign singular perturbation. Appl. Math....
    • 14. Zhou, Y., Wang, J., Zhang, L.: Basic Theory of Fractional Differential Equations. World Scientific, Singapore (2016)
    • 15. Bai, Z., Sun, W.: Existence and multiplicity of positive solutions for singular fractional boundary value problems. Comput. Math. Appl....
    • 16. Tariboon, J., Cuntavepanit, A., Ntouyas, S.K., Nithiarayaphaks, W.: Separated boundary value problems of sequential Caputo and Hadamard...
    • 17. Ahmad, B., Ntouyas, S.K.: Fractional differential inclusions with fractional separated boundary conditions. Fract. Calc. Appl. Anal. 15(3),...
    • 18. Ahmad, B., Ntouyas, S.K., Alsaed, A., Shammakh, W., Agarwal, R.P.: Existence theory for fractional differential equations with non-separated...
    • 19. Agarwal, R.P., Ahmad, B., Alsaedi, A.: Fractional-order differential equations with anti-periodic boundary conditions: a survey. Bound....
    • 20. Benchohra, M., Hamani, S., Ntouyas, S.K.: Boundary value problems for differential equations with fractional order and nonlocal conditions....
    • 21. Goodrich, C.: Existence and uniqueness of solutions to a fractional difference equation with nonlocal conditions. Comput. Math. Appl....
    • 22. Butt, R.L., Alzabut, J., Rehman, U.R., Jonnalagadda, J.: On fractional difference Langevin equations involving non-local boundary conditions....
    • 23. Seemab, A., Rehman, M., Alzabut, J., Hamdi, A.: On the existence of positive solutions for generalized fractional boundary value problems....
    • 24. Ulam, S.M.: A collection of the mathematical problems, pp. 665–666. Interscience, New York (1960)
    • 25. Hyers, D.H.: On the stability of the linear functional equations. Proc. Natl. Acad. Sci. U.S.A. 27(4), 222–224 (1941)
    • 26. Obloza, M.: Hyers stability of the linear differential equation. Rocznik Naukowo-Dydaktyczny Prace Matematyczne 13, 259–270 (1993)
    • 27. Obloza, M.: Connections between Hyers and Lyapunov stability of the ordinary differential equations. Rocznik Naukowo-Dydaktyczny. Prace...
    • 28. Ali, Z., Zada, A., Shah, K.: On Ulam’s stability for a coupled systems of nonlinear implicit fractional differential equations. Bull....
    • 29. Ahmad, M., Jiang, J., Zada, A., Shah, S.O., Xu, J.: Analysis of coupled system of implicit fractional differential equations involving...
    • 30. Riaz, U., Zada, A., Ali, Z., et al.: Analysis of nonlinear coupled systems of impulsive fractional differential equations with Hadamard...
    • 31. Zada, A., Riaz, U., Khan, F.: Hyers-Ulam stability of impulsive integral equations. Boll. Unione Mat. Ital. 12(3), 453–467 (2019)
    • 32. Ntouyas, S.K., Tariboon, J., Sudsutad, W.: Boundary value problems for Riemann–Liouville fractional differential inclusions with nonlocal...
    • 33. Maraaba, T.A., Jarad, F., Baleanu, D.: On the existence and the uniqueness theorem for fractional differential equations with bounded...
    • 34. Almeida, R.: A Caputo fractional derivative of a function with respect to another function. Commun. Nonlinear Sci. Numer Simul. 44, 460–481...
    • 35. Jarad, F., Abdeljawad, T., Baleanu, D.: Caputo-type modification of the Hadamard fractional derivatives. Adv. Differ. Equ. 2012(1), 1–8...
    • 36. Cichon, M., Salem, H.A.H.: On the lack of equivalence between differential and integral forms of the Caputo-type fractional problems....
    • 37. Salem, H.A.H., Cichon, M.: Analysis of tempered fractional calculus in Holder and Orlicz spaces. Symmetry 14, 1581 (2022)
    • 38. Khan, Z.A., Shah, K., Abdalla, B., Abdeljawad, T.: A numerical study of complex dynamics of a chemostat model under fractal-fractional...
    • 39. Ahmed, S., Shah, K., Jahan, S., Abdeljawad, T.: An efficient method for the fractional electric circuits based on Fibonacci wavelet. Results...
    • 40. Shah, K., Abdalla, B., Abdeljawad, T., Gul, R.: Analysis of multipoint impulsive problem of fractionalorder differential equations. Bound....
    • 41. Shah, K., Ali, G., Ansari, K.J., Abdeljawad, T., Meganathan, M., Abdalla, B.: On qualitative analysis of boundary value problem of variable...
    • 42. Acay, B., Bas, E., Abdeljawad, T.: Non-local fractional calculus from different viewpoint generated by truncated M-derivative. J. Comput....
    • 43. Jarad, F., Abdeljawad, T., Baleanu, D.: Caputo-type modification of the Hadamard fractional derivatives. Adv. Differ. Equ. 2012, 1–8 (2012)
    • 44. Adjabi, Y., Jarad, F., Baleanu, D., Abdeljawad, T.: On Cauchy problems with Caputo Hadamard fractional derivatives. J. Comput. Anal. Appl....
    • 45. Bedi, P., Kumar, A., Abdeljawad, T., Khan, A., Gomez-Aguilar, J.F.: Mild solutions of coupled hybrid fractional order system with Caputo–Hadamard...
    • 46. Tajadodi, H., Khan, A., Gomez-Aguilar, J.F., Khan, H.: Optimal control problems with Atangana– Baleanu fractional derivative. Optim. Control...
    • 47. Khan, H., Alzabut, J., Baleanu, D., Alobaidi, G., Rehman, M.: Existence of solutions and a numerical scheme for a generalized hybrid class...
Fundación Dialnet

Mi Documat

Opciones de artículo

Opciones de compartir

Opciones de entorno