Existence and Ulam Hyers Mittag Leffler stability results of $\psi$-Hilfer fuzzy fractional differential equations
Resumen
In the current paper, we investigate a novel class of $\psi$-Hilfer type fuzzy fractional differential equations (FFDEs). Firstly, we convert the system under consideration into an analogous integral system. Secondly, by using Schauder and Banach fixed point theorems, the existence and uniqueness results of solutions for $\psi$-Hilfer FFDEs are then established. Additionally, with aid of generalized Gr$\ddot{o}$nwall inequality, we explore the Ulam–Hyers–Mittag-Leffler stability result of solution for the system under consideration.
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\bibitem{3} Arhrrabi, E., Elomari, M. H., and Melliani, S. Averaging principle for fuzzy stochastic differential equations.
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\bibitem{8}Arhrrabi, E., Elomari, M. H., Melliani, S., and Chadli, L. S. Fuzzy Fractional Boundary Value Problems With Hilfer Fractional Derivatives, Asia Pac. J. Math., 10 (2023), 4. doi:10.28924/APJM/10-4.
\bibitem{9}Hilfer. R, Application of fractional calculus in physics World scientific publishing Co Singapore; 2000.
\bibitem{10}Hilfer R., Experimental evidence for fractional time evolution in glass forming materials, Chemical Physics 284 (2002), 399–408.
\bibitem{11}Hyers DH. On the stability of the linear functional equation. Proc Natl Acad Sci USA 1941;27:222–4.
\bibitem{12}Hyers DH, Isac G, Rassias TM. Stability of functional equations in several variables. Boston: Birkhauser; 1998.
\bibitem{13}Karthikeyan, K., and Karthikeyan, P. Analysis on existence and Mittag-Leffler-Ulam-Hyers-stability results for impulsive psi-Hilfer fractional derivative integro-differential equations. Journal| MESA, (2022), 13(4), 1099-1107.
\bibitem{14} Kilbas, A.A.; Srivastava, H.M.; Trujillo, J.J. Theory and applications of the fractional differential equations. In North-Holland
Mathematics Studies; Elsevier: Amsterdam, The Netherlands, 2006; Volume 204.
\bibitem{15}Liu, K., Wang, J., and O'Regan, D. Ulam–Hyers–Mittag-Leffler stability for $\psi$-Hilfer fractional-order delay differential equations. Advances in Difference Equations, 2019(1), 1-12.
\bibitem{16}Melliani, S., Arhrrabi, E., Elomari, M. H., and Chadli, L. S. (2021). Ulam-Hyers-Rassias stability for fuzzy fractional integrodifferential equations under Caputo gH-differentiability. Int. J. Optim. Appl, 51.
\bibitem{17}Rassias TM. On the stability of the linear mapping in Banach spaces. Proc Amer Math Soc 1978;72:297–300.
\bibitem{18}Ulam SM. Problems in modern mathematics. New York, NY, USA: John Wiley and Sons; 1940.
\bibitem{19}Vu H, Hoa NV. Hyers-Ulam stability of fuzzy fractional Volterra integral equations with the kernel $\psi$-function via successive approximation method. Fuzzy Set Syst 2021;419:67–98.
\bibitem{20}VİVEK, R., VİVEK, D. V., Kangarajan, K., and ELSAYED, E. Some results on the study of-Hilfer type fuzzy fractional differential equations with time delay. Proceedings of International Mathematical Sciences, 4(2), 65-76.
\bibitem{21} Wang, J., Zhou, Y.: Mittag–Leffler–Ulam stabilities of fractional evolution equations. Appl. Math. Lett. 25(4), 723–728 (2012).
\bibitem{22}Wang, X., Luo, D., and Zhu, Q. Ulam-Hyers stability of caputo type fuzzy fractional differential equations with time-delays. Chaos, Solitons and Fractals, (2022) 156, 111822.
\bibitem{23}Zadeh LA. Fuzzy sets. Information and Control 1965;8(3):338-353.
\bibitem{2}Arhrrabi E, Elomari M, Melliani S, Chadli LS. Existence and stability of solutions of fuzzy fractional stochastic differential equations with fractional Brownian motions. Adv Fuzzy Syst 2021;2021:3948493.
\bibitem{3} Arhrrabi, E., Elomari, M. H., and Melliani, S. Averaging principle for fuzzy stochastic differential equations.
\bibitem{4}Arhrrabi, E., Taqbibt, A., Elomari, M. H., Melliani, S., and saadia Chadli, L. (2021, May). Fuzzy fractional boundary value problem. In 2021 7th International Conference on Optimization and Applications (ICOA) (pp. 1-6). IEEE.
\bibitem{5} Arhrrabi, E., Elomari, M., Melliani, S., Chadli, L. S., Existence and Stability of Solutions for a Coupled System of Fuzzy Fractional Pantograph Stochastic Differential Equations, Asia Pac. J. Math., 9 (2022), 20. doi:10.28924/APJM/9-20.
\bibitem{6}Arhrrabi, E., Elomari, M., Melliani, S., Chadli, L. S., Existence and Uniqueness Results of Fuzzy Fractional Stochastic Differential Equations with Impulsive. In International Conference on Partial Differential Equations and Applications, Modeling and Simulation. (2023) (pp. 147-163). Springer, Cham.
\bibitem{7} Arhrrabi, E., Elomari, M. H., Melliani, S., and Chadli, L. S. (2023). Existence and Controllability results for fuzzy neutral stochastic differential equations with impulses. Boletim da Sociedade Paranaense de Matemática, 41, 1-14.
\bibitem{8}Arhrrabi, E., Elomari, M. H., Melliani, S., and Chadli, L. S. Fuzzy Fractional Boundary Value Problems With Hilfer Fractional Derivatives, Asia Pac. J. Math., 10 (2023), 4. doi:10.28924/APJM/10-4.
\bibitem{9}Hilfer. R, Application of fractional calculus in physics World scientific publishing Co Singapore; 2000.
\bibitem{10}Hilfer R., Experimental evidence for fractional time evolution in glass forming materials, Chemical Physics 284 (2002), 399–408.
\bibitem{11}Hyers DH. On the stability of the linear functional equation. Proc Natl Acad Sci USA 1941;27:222–4.
\bibitem{12}Hyers DH, Isac G, Rassias TM. Stability of functional equations in several variables. Boston: Birkhauser; 1998.
\bibitem{13}Karthikeyan, K., and Karthikeyan, P. Analysis on existence and Mittag-Leffler-Ulam-Hyers-stability results for impulsive psi-Hilfer fractional derivative integro-differential equations. Journal| MESA, (2022), 13(4), 1099-1107.
\bibitem{14} Kilbas, A.A.; Srivastava, H.M.; Trujillo, J.J. Theory and applications of the fractional differential equations. In North-Holland
Mathematics Studies; Elsevier: Amsterdam, The Netherlands, 2006; Volume 204.
\bibitem{15}Liu, K., Wang, J., and O'Regan, D. Ulam–Hyers–Mittag-Leffler stability for $\psi$-Hilfer fractional-order delay differential equations. Advances in Difference Equations, 2019(1), 1-12.
\bibitem{16}Melliani, S., Arhrrabi, E., Elomari, M. H., and Chadli, L. S. (2021). Ulam-Hyers-Rassias stability for fuzzy fractional integrodifferential equations under Caputo gH-differentiability. Int. J. Optim. Appl, 51.
\bibitem{17}Rassias TM. On the stability of the linear mapping in Banach spaces. Proc Amer Math Soc 1978;72:297–300.
\bibitem{18}Ulam SM. Problems in modern mathematics. New York, NY, USA: John Wiley and Sons; 1940.
\bibitem{19}Vu H, Hoa NV. Hyers-Ulam stability of fuzzy fractional Volterra integral equations with the kernel $\psi$-function via successive approximation method. Fuzzy Set Syst 2021;419:67–98.
\bibitem{20}VİVEK, R., VİVEK, D. V., Kangarajan, K., and ELSAYED, E. Some results on the study of-Hilfer type fuzzy fractional differential equations with time delay. Proceedings of International Mathematical Sciences, 4(2), 65-76.
\bibitem{21} Wang, J., Zhou, Y.: Mittag–Leffler–Ulam stabilities of fractional evolution equations. Appl. Math. Lett. 25(4), 723–728 (2012).
\bibitem{22}Wang, X., Luo, D., and Zhu, Q. Ulam-Hyers stability of caputo type fuzzy fractional differential equations with time-delays. Chaos, Solitons and Fractals, (2022) 156, 111822.
\bibitem{23}Zadeh LA. Fuzzy sets. Information and Control 1965;8(3):338-353.
Publicado
2025-12-05
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Sección
Research Articles
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