×

Ulam-Hyers-Rassias Mittag-Leffler stability of \(\varpi\)-fractional partial differential equations. (English) Zbl 07917636

MSC:

35R11 Fractional partial differential equations
26A33 Fractional derivatives and integrals
35B35 Stability in context of PDEs

References:

[1] Haubold, H.J., Mathai, A.M., Saxena, R.K.: Mittag-Leffler functions and their applications. J. Appl. Math. 2011 (2011) · Zbl 1218.33021
[2] Podlubny, I., Fractional Differential Equations, 1999, San Diego: Academic Press, San Diego · Zbl 0918.34010
[3] Kilbas, A. A.; Srivastava, H. M.; Trujillo, J. J., Theory and Application of Fractional Differential Equations, 2015, New York: Elsevier, New York
[4] Li, Y.; Chen, Y. Q.; Podlubny, I., Mittag-Leffler stability of fractional order nonlinear dynamic systems, Automatica, 45, 1965-1969, 2009 · Zbl 1185.93062 · doi:10.1016/j.automatica.2009.04.003
[5] Liu, S.; Jiang, W.; Li, X.; Zhou, X., Lyapunov stability analysis of fractional nonlinear systems, Appl. Math. Lett., 51, 13-19, 2016 · Zbl 1356.34061 · doi:10.1016/j.aml.2015.06.018
[6] Hilfer, R., Applications of Fractional Calculus in Physics, 2000, Singapore: World Scientific, Singapore · Zbl 0998.26002 · doi:10.1142/3779
[7] Hyers, D. H., On the stability of the linear functional equation, Proc. Natl. Acad. Sci., 27, 222-224, 1941 · Zbl 0061.26403 · doi:10.1073/pnas.27.4.222
[8] Rassias, T. M., On the stability of linear mappings in Banach spaces, Proc. Am. Math. Soc., 72, 297-300, 1978 · Zbl 0398.47040 · doi:10.1090/S0002-9939-1978-0507327-1
[9] Hyers, D. H.; Isac, G.; Rassias, T. M., Stability of Functional Equations in Several Variables, 1998, Basel: Birkh Auser, Basel · Zbl 0907.39025 · doi:10.1007/978-1-4612-1790-9
[10] Seemab, A., On the existence and Ulam-Hyers stability of a new class of partial \((\phi ,\varpi )\)-fractional differential equations with impulses, Filomat, 35, 6, 1977-1991, 2021 · doi:10.2298/FIL2106977S
[11] Makhlouf, A. B.; Boucenna, D., Ulam-Hyers-Rassias Mittag-Leffler stability for the Darboux problem for partial fractional differential equations, Rocky Mt. J. Math., 51, 5, 1541-1551, 2021 · Zbl 1490.35035
[12] Guo, Y.; Chen, M.; Shu, X.-B.; Xu, F., The existence and Hyers-Ulam stability of solution for almost periodical fractional stochastic differential equation with fBm, Stoch. Anal. Appl., 39, 4, 643-666, 2021 · Zbl 1484.34021 · doi:10.1080/07362994.2020.1824677
[13] Aderyani, S. R.; Saadati, R.; Yang, X. J., Radu-Miheţ method for UHML stability for a class of ξ-Hilfer fractional differential equations in matrix valued fuzzy Banach spaces, Math. Methods Appl. Sci., 44, 14619-14631, 2021 · Zbl 1485.34016 · doi:10.1002/mma.7730
[14] Aderyani, S. R.; Saadati, R.; O’Regan, D.; Abdeljawad, T., UHML stability of a class of Δ-Hilfer FDEs via CRM, AIMS Math., 7, 5910-5919, 2022 · doi:10.3934/math.2022328
[15] Aderyani, S. R.; Saadati, R.; Fečkan, M., The Cădariu-Radu method for existence, uniqueness and Gauss hypergeometric stability of Ω-Hilfer fractional differential equations, Mathematics, 9, 2021 · doi:10.3390/math9121408
[16] Ben Makhlouf, A.; Benjemaa, M.; Boucenna, D.; Mchiri, L.; Rhaima, M., On generalized proportional fractional order derivatives and Darboux problem for partial differential equations, Discrete Dyn. Nat. Soc., 2023, 1-22, 2023 · Zbl 07915486 · doi:10.1155/2023/6648524
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.