Non-instantaneous impulsive fractional integro-differential inclusions with state-dependent delay
Khalida Aissaniaissani_k@yahoo.frLaboratory of MathematicsUniversity of Sidi Bel-AbbèsSidi Bel-Abbès, P. O. Box 89, 22000, Algeria0000-0002-7065-6043View full profile → , *Abdelkrim SalimCorresponding authorsalim.abdelkrim@yahoo.coma.salim@univ-chlef.dzAffiliation 1Faculty of TechnologyHassiba Benbouali UniversityChlef, P. O. Box 151, 02000, AlgeriaAffiliation 2Laboratory of MathematicsUniversity of Sidi Bel-AbbèsSidi Bel-Abbès, P. O. Box 89, 22000, Algeria0000-0003-2795-6224View full profile → , Mouffak Benchohrabenchohra@yahoo.comLaboratory of MathematicsUniversity of Sidi Bel-AbbèsSidi Bel-Abbès, P. O. Box 89, 22000, Algeria0000-0003-3063-9449View full profile →
* Corresponding author · click or hover a name for details
- Received:
- 08 Nov 2022
- Published Online:
- 09 Dec 2025
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIOS-1515
- Pages:
- 215–233
Abstract
Keywords
Subject Classifications
References
[1] S. Abbas, B. Ahmad, M. Benchohra, and A. Salim, Fractional Difference, Differential Equations and Inclusions: Analysis and Stability, Morgan Kaufmann, Cambridge (2024). doi:10.1016/C2023-0-00030-9.
[2] K. Aissani and M. Benchohra, “Impulsive fractional differential inclusions with infinite delay,” Electron. J. Differential Equations, vol. 2013, no. 265, pp. 1–13 (2013).
[3] K. Aissani, M. Benchohra, and K. Ezzinbi, “Fractional integro-differential inclusions with state-dependent delay,” in Differential Inclusions, Control and Optimization, vol. 34, pp. 153–167, 2014.
[4] K. Aissani, M. Benchohra, and M. A. Darwish, “Semilinear fractional order integro-differential inclusions with infinite delay,” Georgian Math. J., vol. 25, pp. 317–327 (2017).
[5] D. Baleanu, K. Diethelm, E. Scalas, and J. J. Trujillo, Fractional Calculus: Models and Numerical Methods, World Scientific Publishing, New York (2012).
[6] M. Benchohra, F. Bouazzaoui, E. Karapnar, and A. Salim, “Controllability of second order functional random differential equations with delay,” Mathematics, vol. 10, pp. 1–16 (2022). doi:10.3390/math10071120.
[7] M. Benchohra, S. Bouriah, A. Salim, and Y. Zhou, Fractional Differential Equations: A Coincidence Degree Approach, Berlin, Boston: De Gruyter (2024). doi:10.1515/9783111334387.
[8] M. Benchohra, E. Karapnar, J. E. Lazreg, and A. Salim, Advanced Topics in Fractional Differential Equations: A Fixed Point Approach, Cham: Springer (2023). doi:10.1007/978-3-031-26928-8.
[9] M. Benchohra, E. Karapnar, J. E. Lazreg, and A. Salim, Fractional Differential Equations: New Advancements for Generalized Fractional Derivatives, Cham: Springer (2023). doi:10.1007/978-3-031-34877-8.
[10] M. Benchohra, G. N’Guérékata, and A. Salim, Advanced Topics on Semilinear Evolution Equations, Hackensack, NJ: World Scientific (2025). doi:10.1142/14092.
[11] M. Benchohra, A. Salim, and Y. Zhou, Integro-Differential Equations: Analysis, Stability and Controllability, Berlin, Boston: De Gruyter (2024). doi:10.1515/9783111437910.
[12] N. Benkhettou, K. Aissani, A. Salim, M. Benchohra, and C. Tunc, “Controllability of fractional integro-differential equations with infinite delay and non-instantaneous impulses,” Appl. Anal. Optim., vol. 6, pp. 79–94 (2022).
[13] N. Benkhettou, A. Salim, K. Aissani, M. Benchohra, and E. Karapnar, “Non-instantaneous impulsive fractional integro-differential equations with state-dependent delay,” Sahand Commun. Math. Anal., vol. 19, pp. 93–109 (2022). doi:10.22130/scma.2022.542200.1014.
[14] A. Bensalem, A. Salim, M. Benchohra, and G. N’Guérékata, “Functional integro-differential equations with state-dependent delay and non-instantaneous impulsions: existence and qualitative results,” Fractal Fract., vol. 6, pp. 1–27 (2022). doi:10.3390/fractalfract6100615.
[15] S. Bouriah, A. Salim, and M. Benchohra, “On nonlinear implicit neutral generalized Hilfer fractional differential equations with terminal conditions and delay,” Topol. Algebra Appl., vol. 10, pp. 77–93 (2022). doi:10.1515/taa-2022-0115.
[16] A. Cernea, “On a fractional differential inclusion with boundary condition,” Studia Univ. Babes-Bolyai Mathematica, vol. LV, pp. 105–113 (2010).
[17] L. Debnath and D. Bhatta, Integral Transforms and Their Applications, 2nd ed., CRC Press (2007).
[18] K. Deimling, Multivalued Differential Equations, Berlin-New York: Walter De Gruyter (1992).
[19] K. Diethelm, The Analysis of Fractional Differential Equations, Berlin: Springer (2010).
[20] J. Dugundji and A. Granas, Fixed Point Theory, New York: Springer-Verlag (2003).
[21] A. M. A. El-Sayed and A. G. Ibrahim, “Multivalued fractional differential equations of arbitrary orders,” Appl. Math. Comput., vol. 68, pp. 15–25 (1995).
[22] G. R. Gautam and J. Dabas, “Existence result of fractional functional integro-differential equation with not instantaneous impulse,” Int. J. Adv. Appl. Math. Mech., vol. 1, no. 3, pp. 11–21 (2014).
[23] L. Górniewicz, Topological Fixed Point Theory of Multivalued Mappings, Mathematics and its Applications, vol. 495, Dordrecht: Kluwer Academic Publishers (1999).
[24] J. K. Hale and J. Kato, “Phase space for retarded equations with infinite delay,” Funk. Ekvacioj, vol. 21, pp. 11–41 (1978).
[25] A. Heris, A. Salim, M. Benchohra, and E. Karapnar, “Fractional partial random differential equations with infinite delay,” Results in Physics (2022). doi:10.1016/j.rinp.2022.105557.
[26] E. Hernández and D. O’Regan, “On a new class of abstract impulsive differential equations,” Proc. Amer. Math. Soc., vol. 141, pp. 1641–1649 (2013).
[27] E. Hernández, A. Prokopczyk, and L. Ladeira, “A note on partial functional differential equations with state-dependent delay,” Nonlinear Anal. RWA, vol. 7, pp. 510–519 (2006).
[28] Y. Hino, S. Murakami, and T. Naito, Functional Differential Equations with Unbounded Delay, Berlin: Springer-Verlag (1991).
[29] Sh. Hu and N. Papageorgiou, Handbook of Multivalued Analysis, Volume I: Theory, Dordrecht, Boston, London: Kluwer Academic Publishers (1997).
[30] A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Amsterdam: Elsevier Science B.V. (2006).
[31] S. Krim, A. Salim, S. Abbas, and M. Benchohra, “On implicit impulsive conformable fractional differential equations with infinite delay in b-metric spaces,” Rend. Circ. Mat. Palermo (2), pp. 1–14 (2022). doi:10.1007/s12215-022-00818-8.
[32] P. Kumar, R. Haloi, D. Bahuguna, and D. N. Pandey, “Existence of solutions to a new class of abstract non-instantaneous impulsive fractional integro-differential equations,” Nonlin. Dynam. Syst. Theor., vol. 16, no. 1, pp. 73–85 (2016).
[33] A. Lachouri, A. Ardjouni, and A. Djoudi, “Investigation of the existence and uniqueness of solutions for higher order fractional differential inclusions and equations with integral boundary conditions,” J. Interdiscip. Math., vol. 24, no. 8, pp. 2161–2179 (2021). doi:10.1080/09720529.2021.1877901.
[34] A. Lasota and Z. Opial, “An application of the Kakutani-Ky Fan theorem in the theory of ordinary differential equations,” Bull. Acad. Pol. Sci. Ser. Sci. Math. Astronom. Phys., vol. 13, pp. 781–786 (1965).
[35] J. E. Lazreg, M. Benchohra, and A. Salim, “Existence and Ulam stability of k-generalized ψ-Hilfer fractional problem,” J. Innov. Appl. Math. Comput. Sci., vol. 2, pp. 01–13 (2022).
[36] P. Li and C. J. Xu, “Mild solution of fractional order differential equations with not instantaneous impulses,” Open Math., vol. 13, pp. 436–443 (2015).
[37] F. Mainardi, P. Paradisi, and R. Gorenflo, “Probability distributions generated by fractional diffusion equations,” in Econophysics: An Emerging Science, J. Kertesz and I. Kondor, Eds., Dordrecht, The Netherlands: Kluwer Academic Publishers (2000).
[38] D. N. Pandey, S. Das, and N. Sukavanam, “Existence of solution for a second-order neutral differential equation with state dependent delay and non-instantaneous impulses,” Int. J. Nonlin. Sci., vol. 18, no. 2, pp. 145–155 (2014).
[39] I. Podlubny, Fractional Differential Equations, New York, NY: Academic Press (1993).
[40] A. Salim, S. Abbas, M. Benchohra, and E. Karapnar, “A Filippov’s theorem and topological structure of solution sets for fractional q-difference inclusions,” Dynam. Systems Appl., vol. 31, pp. 17–34 (2022). doi:10.46719/dsa202231.01.02.
[41] A. Salim, B. Ahmad, M. Benchohra, and J. E. Lazreg, “Boundary value problem for hybrid generalized Hilfer fractional differential equations,” Differ. Equ. Appl., vol. 14, pp. 379–391 (2022). doi:10.7153/dea-2022-14-27.
[42] A. Salim, M. Benchohra, J. R. Graef, and J. E. Lazreg, “Initial value problem for hybrid ψ-Hilfer fractional implicit differential equations,” J. Fixed Point Theory Appl., vol. 24, pp. 1–14 (2022). doi:10.1007/s11784-021-00920-x.
[43] S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, Yverdon: Gordon and Breach (1993).
[44] V. E. Tarasov, Fractional Dynamics: Application of Fractional Calculus to Dynamics of Particles, Fields and Media, Heidelberg: Springer; Beijing: Higher Education Press (2010).
