On Periodic solutions for implicit nonlinear Caputo tempered fractional differential problems

• Autorzy: Bouriah Soufyane , Salim Abdelkrim , Benchohra Mouffak , Karapinar Erdal

Identyfikatory

DOI

10.1515/dema-2023-0154

• Języki publikacji: EN

Abstrakty

EN

The main goal of this article is to study the existence and uniqueness of periodic solutions for the implicit problem with nonlinear fractional differential equation involving the Caputo tempered fractional derivative. The proofs are based upon the coincidence degree theory of Mawhin. To show the efficiency of the stated result, two illustrative examples will be demonstrated.

Słowa kluczowe

EN

coincidence degree theory; existence; uniqueness; tempered fractional operators; implicit problems

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2024
• Tom: Vol. 57, nr 1
• Strony: art. no. 20230154
• Opis fizyczny: Bibliogr. 26 poz.

Twórcy

autor

Bouriah Soufyane

• Department of Mathematics, Faculty of Exact Sciences and Informatics, University Hassiba Benbouali of Chlef, Chlef, Algeria

autor

Salim Abdelkrim

• Faculty of Technology, Hassiba Benbouali University of Chlef, P.O. Box 151, Chlef 02000, Algeria
• Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbes, P.O. Box 89, Sidi Bel-Abbes 22000, Algeria

autor

Benchohra Mouffak

• Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbes, P.O. Box 89, Sidi Bel-Abbes 22000, Algeria

autor

Karapinar Erdal

• Department of Mathematics, Çankaya University, Ankara, Turkey
• Department of Medical Research, China Medical University Hospital, China Medical University, 40402, Taichung, Taiwan

Bibliografia

• [1] R. Herrmann, Fractional Calculus: An Introduction for Physicists, World Scientific Publishing Company, Singapore, 2011.
• [2] S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives. Theory and Applications, Gordon and Breach, Yverdon, 1993.
• [3] M. Benchohra, E. Karapınar, J. E. Lazreg, and A. Salim, Advanced Topics in Fractional Differential Equations: A Fixed Point Approach, Springer, Cham, 2023.
• [4] M. Benchohra, E. Karapınar, J. E. Lazreg and A. Salim, Fractional Differential Equations: New Advancements for Generalized Fractional Derivatives, Springer, Cham, 2023.
• [5] R. E. Gaines and J. Mawhin, Coincidence degree and nonlinear differential equations, Lecture Notes in Mathematics, Springer-Verlag, Berlin, 1977.
• [6] J. Mawhin, NSFCBMS Regional Conference Series in Mathematics, American Mathematical Society, Providence, RI, 1979.
• [7] D. Benzenati, S. Bouriah, A. Salim, and M. Benchohra, On periodic solutions for some nonlinear fractional pantograph problems with Ψ-Hilfer derivative, Lobachevskii J. Math. 44 (2023), 1264–1279, DOI: https://doi.org/10.1134/S1995080223040054.
• [8] S. Bouriah, D. Foukrach, M. Benchohra, and J. Graef, Existence and uniqueness of periodic solutions for some nonlinear fractional pantograph differential equations with ψ-Caputo derivative, Arab. J. Math. 10 (2021), no. 3, 575–587.
• [9] S. Bouriah, M. Benchohra, J. Nieto, and Y. Zhou, Ulam stability for nonlinear implicit differential equations with Hilfer-Katugampola fractional derivative and impulses, AIMS. Math. 7 (2022), no. 7, 12859–12884.
• [10] S. Bouriah, A. Salim, and M. Benchohra, On nonlinear implicit neutral generalized Hilfer fractional differential equations with terminal conditions and delay, Topol. Algebra Appl. 10 (2022), no. 1, 77–93.
• [11] M. Chohri, S. Bouriah, A. Salim, and M. Benchohra, On nonlinear periodic problems with Caputo’s exponential fractional derivative, ATNAA. 7 (2023), 103–120, DOI: https://doi.org/10.31197/atnaa.1130743.
• [12] D. Foukrach, S. Bouriah, M. Benchohra, and E. Karapinar, Some new results for ψ-Hilfer fractional pantograph-type differential equation depending on ψ-Riemann-Liouville integral, J. Anal. 30 (2021), no. 1, 195–219.
• [13] A. Salim, M. Benchohra, and J. E. Lazreg, On implicit k -generalized ψ-Hilfer fractional differential coupled systems with periodic conditions, Qual. Theory Dyn. Syst. 22 (2023), 46, DOI: https://doi.org/10.1007/s12346-023-00776-1.
• [14] A. Salim, S. Bouriah, M. Benchohra, J. E. Lazreg, and E. Karapınar, A study on k -generalized ψ-Hilfer fractional differential equations with periodic integral conditions, Math. Methods Appl. Sci. (2023), 1–18, DOI: https://doi.org/10.1002/mma.9056.
• [15] R. G. Buschman, Decomposition of an integral operator by use of Mikusinski calculus, SIAM J. Math. Anal. 3 (1972), 83–85.
• [16] R. Almeida and M. L. Morgado, Analysis and numerical approximation of tempered fractional calculus of variations problems, J. Comput. Appl. Math. 361 (2019), 1–12.
• [17] S. Krim, A. Salim, and M. Benchohra, Nonlinear contractions and Caputo-tempered implicit fractional differential equations in b-metric spaces with infinite delay, Filomat. 37 (2023), no. 22, 7491–7503, DOI: https://doi.org/10.2298/FIL2322491K.
• [18] S. Krim, A. Salim, and M. Benchohra, On implicit Caputo-tempered fractional boundary value problems with delay, Lett. Nonlinear Anal. Appl. 1 (2023), no. 1, 12–29, DOI: https://doi.org/10.5281/zenodo.7682064.
• [19] C. Li, W. Deng, and L. Zhao, Well-posedness and numerical algorithm for the tempered fractional differential equations, Discr. Contin. Dyn. Syst. Ser. B. 24 (2019), 1989–2015.
• [20] M. Medved and E. Brestovanska, Differential equations with tempered ψ-Caputo fractional derivative, Math. Model. Anal. 26 (2021), 631–650.
• [21] N. A. Obeidat and D. E. Bentil, New theories and applications of tempered fractional differential equations, Nonlinear Dyn. 105 (2021), 1689–1702.
• [22] A. Salim, S. Krim, J. E. Lazreg, and M. Benchohra, On Caputo-tempered implicit fractional differential equations in b-metric spaces, Analysis. 43 (2023), no. 2, 129–139, DOI: https://doi.org/10.1515/anly-2022-1114.
• [23] B. Shiri, G. Wu, and D. Baleanu, Collocation methods for terminal value problems of tempered fractional differential equations, Appl. Numer. Math. 156 (2020), 385–395.
• [24] F. Sabzikar, M. M. Meerschaert, and J. Chen, Tempered fractional calculus, J. Comput. Phys. 293 (2015), 14–28.
• [25] A. Mali, K. Kucche, A. Fernandez, and H. Fahad, On tempered fractional calculus with respect to functions and the associated fractional differential equations, Math. Methods Appl. Sci. 45 (2022), no. 17, 11134–11157.
• [26] D. O’Regan, Y. J. Chao, and Y. Q. Chen, Topological Degree Theory and Application, Taylor and Francis Group, Boca Raton, London, New York, 2006.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).