Implicit Caputo-Katugampola Fractional Problems with Infinite Delay and Impulses

Authors

Salim Krim Ecole National Supérieure d'Oran, BP 1063 SAIM MOHAMED, Oran 31003, Algeria; Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbes, P.O. Box 89 Sidi Bel-Abbes 22000, Algeria
Abdelkrim Salim Faculty of Technology, Hassiba Benbouali University of Chlef, P.O. Box 151 Chlef 02000, Algeria; bLaboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbes, P.O. Box 89 Sidi Bel-Abbes 22000, Algeria Corresponding Author
Saïd Abbas bLaboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbes, P.O. Box 89 Sidi Bel-Abbes 22000, Algeria
Mouffak Benchohra Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbes, P.O. Box 89 Sidi Bel-Abbes 22000, Algeria

Keywords:

Caputo-Katugampola fractional order derivative, infinite delay, Schaefer's fixed point theorem, Nonlocal impulsive

Abstract

This paper deals with some existence results for a class of Caputo-Katugampola implicit impulsive fractional differential equations with infinite delay. The results are based on the Schaefer's fixed point theorem. We illustrate our results by an example in the last section.

References

[1] H. Afshari, H. Aydi, E. Karapinar, Existence of fixed points of set-valued mappings in b-metric spaces, East Asian Math. J. 32 (3) (2016), 319-332.

[2] H. Afshari, H. Aydi, E. Karapinar, On generalized α − ψ−Geraghty contractions on b-metric spaces, Georgian Math. J. 27(1) (2020), 9-21.

[3] R. Almeida, A. B. Malinowska and T. Odzijewicz, Fractional differential equations with dependence on the Caputo- Katugampola derivative, J. Comput Nonlinear Dynam. 11 (6) (2016), 11 pages.

[4] Y. Arioua, B. Basti, N. Benhamidouche, Initial value problem for nonlinear implicit fractional differential equations with Katugampola derivative, Appl. Math. E-Notes 19 (2019), 397-412.

[5] M. Benchohra, F. Bouazzaoui, E. Karapınar and A. Salim, Controllability of second order functional random differential equations with delay. Mathematics. 10 (2022), 16pp. https://doi.org/10.3390/math10071120

[6] M. Benchohra, S. Bouriah, A. Salim and Y. Zhou, Fractional Differential Equations: A Coincidence Degree Approach, Berlin, Boston: De Gruyter, 2024. https://doi.org/10.1515/9783111334387

[7] M. Benchohra, E. Karapınar, J. E. Lazreg and A. Salim, Advanced Topics in Fractional Differential Equations: A Fixed Point Approach, Springer, Cham, 2023. https://doi.org/10.1007/978-3-031-26928-8

[8] M. Benchohra, E. Karapınar, J. E. Lazreg and A. Salim, Fractional Differential Equations: New Advancements for Generalized Fractional Derivatives, Springer, Cham, 2023. https://doi.org/10.1007/978-3-031-34877-8

[9] J. Hale and J. Kato, Phase space for retarded equations with infinite delay, Funkcial. Ekvac. 21 (1978), 11-41.

[10] A. Heris, A. Salim, M. Benchohra and E. Karapınar, Fractional partial random differential equations with infinite delay. Results in Physics. (2022). https://doi.org/10.1016/j.rinp.2022.105557

[11] E. Karapinar, C. Chifu, Results in wt-distance over b-metric spaces, Math. 8 (2020).

[12] E. Karapinar, A. Fulga, A. Petrusel, On Istratescu type contractions in b-metric spaces, Math. 8 (2020). https://doi.org/10.3390/math8030388

[13] E. Karapinar, A. Fulga, Fixed point on convex b-metric space via admissible mappings, TWMS J. Pure Appl. Math. 12 (2021), no. 2, 254–264.

[14] U. N. Katugampola, A new approach to generalized fractional derivatives, Bull. Math. Anal. Appl. 6 (2014), 1–15.

[15] U. N. Katugampola, New approach to a generalized fractional integral, Appl. Math. Comput. 218 (2011), 860–865.

[16] A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier Science B.V., Amsterdam, 2006.

[17] 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). (2022), 1-14. https://doi.org/10.1007/s12215-022-00818-8

[18] S. Krim, A. Salim and M. Benchohra, On implicit Caputo tempered fractional boundary value problems with delay. Lett. Nonlinear Anal. Appl. 1 (1) (2023), 12-29. https://doi.org/10.5281/zenodo.7682064

[19] K. D. Kucche, J. J. Nieto, V. Venktesh, V. Theory of nonlinear implicit fractional differential equations. Differ. Equ. Dynam. Syst. 28 (2020), 1–17.

[20] A. Salim, S. Abbas, M. Benchohra and E. Karapınar, A Filippov’s theorem and topological structure of solution sets for fractional q-difference inclusions. Dynam. Systems Appl. 31 (2022), 17-34. https://doi.org/10.46719/dsa202231.01.02

[21] A. Salim, B. Ahmad, M. Benchohra and J. E. Lazreg, Boundary value problem for hybrid generalized Hilfer fractional differential equations, Differ. Equ. Appl. 14 (2022), 379-391. http://dx.doi.org/10.7153/dea-2022-14-27

[22] A. Salim and M. Benchohra, A study on tempered (k, ψ)-Hilfer fractional operator, Lett. Nonlinear Anal. Appl. 1 (3) (2023), 101-121. https://doi.org/10.5281/zenodo.8361961

[23] A. Salim, M. Benchohra, J. E. Lazreg and G. N’Gu´er´ekata, Existence and k-Mittag-Leffler-Ulam-Hyers stability results of k-generalized ψ-Hilfer boundary value problem. Nonlinear Studies. 29 (2022), 359–379.

[24] S. G. Samko, A. A. Kilbas and O. I. Marichev, Fractional Integrals and Derivatives. Theory and Applications, Gordon and Breach, Amsterdam, 1987, Engl. Trans. from the Russian.

[25] V. E. Tarasov, Fractional Dynamics: Application of Fractional Calculus to Dynamics of Particles, Fields and Media, Springer, Heidelberg; Higher Education Press, Beijing, 2010.

[26] A. N. Vityuk and A. V. Mykhailenko, The Darboux problem for an implicit fractional-order differential equation, J. Math. Sci. 175 (4) (2011), 391-401.

[27] Y. Zhou, Basic Theory of Fractional Differential Equations, World Scientific, Singapore, 2014.

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