Existence and Stability results of the solution for nonlinear fractional differential problem

  • Naimi Abdellouahab Kasdi Merbah University
  • Brahim Tellab Kasdi Merbah University
  • Khaled Zennir AL-Ras Qassim University

Résumé

The problem of existence and stability results for fractional problem is considered. Based on the Krasnoselskii's fixed point theorem, we prove our main results. Then we give an examples to illustrate our main results.

Téléchargements

Les données sur le téléchargement ne sont pas encore disponible.

Références

N. Abdellouahab, B. Tellab and Kh. Zennir, Existence and Stability results of a nonlinear fractional integro-differential equation with integral boundary conditions, Kragujevac J. Math., 46(2), (2022), 685-699. DOI: https://doi.org/10.46793/KgJMat2205.685A

N. Abdellouahab, B. Tellab and Kh. Zennir, Existence and Stability results for the solution of Neutral fractional integro-differential equation with nonlocal conditions, (2019), submitted.

B. Ahmed, A. Alsaedi, S. Salem and S. K. Ntouyas, Fractional Differential Equation Involving Mixed Nonlinearities with Nonlocal multi-point and Reimann-steiljes integral-multi-strip conditions, Fractal Fract., 34(3), (2019). https://doi.org/10.3390/fractalfract3020034 DOI: https://doi.org/10.3390/fractalfract3020034

T. M. Atanackovic, B. Stankovic, On a differential equation with left and right fractional derivatives, Fractional calc. Appl. Anal., 10(2), (2007), 139-150.

T. A. Burton, Stability by Fixed Point Theory for Functional Differential Equations, Dover publications INC, Mineola, New York, 2006.

F. Ge, C. Kou, Stability analysis by Krasnoselskii's fixed point theorem for nonlinear fractional differential equations, Appl. Math. Comput., 257, (2015), 308-316. https://doi.org/10.1016/j.amc.2014.11.109 DOI: https://doi.org/10.1016/j.amc.2014.11.109

A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and applications of fractional differential equations. Elsevier, Amsterdam, 539,(2006).

C. Kou, H. Zhou, Y. Yan, Existence of solutions of initial value problems for nonlinear fractional differential equations on the half-axis, Nonl. Anal., 74, (2011), 5975-5986. https://doi.org/10.1016/j.na.2011.05.074 DOI: https://doi.org/10.1016/j.na.2011.05.074

M. A. Kranoselskii, Two remarks on the method of successive approximations. Uspekhi Mat. Nauk., 10, (1955), 123-127.

B. Stankovic, An equation with left and right fractional derivatives, Publications de l'institute mathematique, Nouvelle serie, 80(94), (2006), 259-272. https://doi.org/10.2298/PIM0694259S DOI: https://doi.org/10.2298/PIM0694259S

Y. Zhou, Basic theory of fractional differential equations, 6, Singapore: World Scientific, (2014). https://doi.org/10.1142/9069 DOI: https://doi.org/10.1142/9069

Publiée
2022-12-21
Rubrique
Articles