Solvability and stability for fractional differential equations involving two Riemann-Liouville fractional orders
*M. HouasCorresponding authorhouas.mohamed@yahoo.frDepartment of MathematicsFaculty of Sciences and TechnologyKhemis Miliana UniversityKhemis Miliana, AlgeriaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 08 Oct 2019
- Accepted:
- 13 Apr 2020
- Published Online:
- 29 Dec 2023
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-1096
- Pages:
- 1699–1715
Abstract
Keywords
Subject Classifications
References
[1] Z. Andras, A.R. Meszaros, Ulam-Hyers stability of dynamic equations on time scales via Picard operators. Appl. Math. Comput. 219, (2013), 4853-4864.
[2] Z. Bai, H. Lu, Langevin differential equation of fractional order in non compactness Banach space. J. Math. Anal. Appl. 311, (2005), 495-505.
[3] M. Bezziou, Z. Dahmani and A. Ndiaye, Existence and Ulam stability for nonlinear implicit fractional di erential equations with Hadamard derivative. J. Interdisciplinary Mathematics. 23(4), 857-876, (2020).
[4] Z. Cui, P. Yu and Z. Mao, Existence of solutions for nonlocal boundary value problems of nonlinear fractional differential equations. Adv. Dyn. Sys. Appl. 7(1), (2012), 31-40.
[5] Z. Dahmani, S. Belarbi, New results for fractional evolution equations using Banach fixed point theorem. Int. J. Nonlinear Anal. Appl. 5(2) (2014), 22-30.
[6] Z. Dahmani, L. Tabharit, Fractional order differential equations involving Caputo derivative. Theory Appl. Math. Comput. Sci. 4(1) (2014), 40-55.
[7] A. Granas and J. Dugundji, Fixed point theory. Springer-Verlas, New York. 2003.
[8] S. Ferraoun, Z. Dahman, Existence and stability of solutions of a class of hybrid fractional differential equations involving RL-operator. J. Interdisciplinary Mathematics. 23(4), 885-903, (2020).
[9] M. Houas, Z. Dahmani, New results for a coupled system of fractional differential equations. Facta. Univ. Ser. Math. Inform. 28(2) (2013), 133-150.
[10] M. Houas, Z. Dahmani, New results for a system of two fractional differential equations involving n Caputo derivatives. Kragujevac. J. Math. 38 (2014), 283-301.
[11] M. Houas, Z. Dahmani, On existence of solutions for fractional differential equations with nonlocal multi-point boundary conditions. Lobachevskii. J. Math. 37(2) (2016), 120-127.
[12] M. Houas and M. Bezziou, Existence and stability results for fractional differential equations with two Caputo fractional derivatives. Facta Univ. Ser. Math. Inform. 34(2) (2019), 341-357.
[13] M. Houas, Existence and uniqueness results for a coupled system of nonlinear fractional differential equations with two fractional orders. Accepted in J. Interdisciplinary Mathematics.
[14] R.W. Ibrahim. Ulam stability of boundary value problem. Kragujevac. J. Math. 37(2) (2013), 287-297.
[15] A.A. Kilbas, S.A. Marzan. Nonlinear differential equation with the Caputo fraction derivative in the space of continuously differentiable functions. Differ. Equ. 41(1), (2005), 84-89.
[16] N. Lungu, D. Popa, Hyers-Ulam stability of a first order partial differential equation. J. Math. Anal. Appl. 385 (2012), 86-91.
[17] A. Saadi, M. Benbachir. Positive solutions for three-point nonlinear fractional boundary value problems. Electron. J. Qual. Theory Differ. Equ. 2 (2011), 1-19.
[18] A. Taieb, Z. Dahmani, The hight order Lane-Emden fractional differential system: existence, uniqueness and Ulam type stabilities. Kragujevac. J. Math. 40(2) (2016), 238-259.
[19] J. Tariboon, S.K. Ntouyas and C. Thaiprayoon, Nonlinear Langevin equation of Hadamard-Caputo type fractional derivatives with nonlocal fractional integral conditions. Adv. Math. Ph. Volume 2014 . Article ID 372749, (2014), 1-15.
[20] C. Thaiprayoon, S.K. Ntouyas and J. Tariboon. On the nonlocal Katugampola fractional integral conditions for fractional Langevin equation. Adv. Difference. Equ. 374 (2015), 1-16.
[21] J. Wang, L. Lv and Y. Zhou. Ulam stability and data dependence for fractional differential equations with Caputo derivative. Electron. J. Qual. Theory Differ. Equ. 63, (2011), 1-10.
[22] W. Yukunthorn, S.K. Ntouyas and J. Tariboon. Nonlinear fractional Caputo-Langevin equation with nonlocal Riemann-Liouville fractional integral conditions. Adv. Difference. Equ. 315 (2014), 1-18.
[23] G. Wang, W. Liu and C. Ren, Existence of solutions for multi-point nonlinear differential equations of fractional orders with integral boundary conditions. Electron. J. Differ. Equ. 54 (2012), 1-10.




