Uniqueness Results for Fractional Integro-differential Equations with State-Dependent Nonlocal Conditions in Fréchet Spaces

[1] R. P. Agarwal, B. Andradec, G. Siracusa, On fractional integro-differential equations with state-dependent delay, Comput. Math. Appl. 63 (3) (2011), 1142-1149.Search in Google Scholar

[2] J. C. Alvárez, Measure of noncompactness and fixed points of nonexpansive condensing mappings in locally convex spaces, Rev. Real. Acad. Cienc. Exact. Fis. Natur., Madrid, 79 (1985), 53-66.Search in Google Scholar

[3] A. Anguraj, P. Karthikeyan, J. J. Trujillo, Existence of solutions to fractional mixed integro-differential equations with nonlocal initial condition, Adv. Difference Equ. 2011, Art. ID 690653, 12 pp.Search in Google Scholar

[4] W. Arendt, C. Batty, M., Hieber, F. Neubrander, Vector-Valued Laplace Transforms and Cauchy Problems, Monographs in Mathematics, 96 Birkhauser, Basel, 2001.Search in Google Scholar

[5] K. Balachandran, S. Kiruthika, J. J. Trujillo, Existence results for fractional impulsive integro-differential equations in Banach spaces, Commun. Nonlinear Sci. Numer. Simul. 16 (2011), 1970-1977.Search in Google Scholar

[6] A. Belarbi, M. Benchohra, A. Ouahab, Uniqueness results for fractional functional differential equations with infinite delay in Fréchet spaces, Applicable Analysis 85 (12) (2006), 1459-1470.Search in Google Scholar

[7] M. Benchohra, F. Bouazzaoui, E. Karapinar, A. Salim, Controllability of second order functional random differential equations with delay, Mathematics 10 (2022), 16pp, https://doi.org/10.3390/math10071120Search in Google Scholar

[8] N. Benkhettou, K. Aissani, A. Salim, M. Benchohra, C. Tunc, Controllability of fractional integro-differential equations with infinite delay and non-instantaneous impulses, Appl. Anal. Optim. 6 (2022), 79-94.Search in Google Scholar

[9] S. Bouriah, A. Salim, M. Benchohra, On nonlinear implicit neutral generalized Hilfer fractional differential equations with terminal conditions and delay, Topol. Algebra Appl. 10 (2022), 77-93, https://doi.org/10.1515/taa-2022-0115Search in Google Scholar

[10] L. Byszewski, Existence, uniqueness and asymptotic stability of solutions of abstract nonlocal Cauchy problems, Dynam. Systems Appl. 5 (1996), 595-605.Search in Google Scholar

[11] L. Byszewski, H. Akca, Existence of solutions of a semilinear functional differential evolution nonlocal problem, Nonlinear Anal. 34 (1998), 65-72.Search in Google Scholar

[12] C. Cuevas, J.-C. de Souza, S-asymptotically w-periodic solutions of semilinear fractional integro-differential equations, Appl. Math. Lett. 22 (2009), 865-870.Search in Google Scholar

[13] C. Derbazi, H. Hammouche, A. Salim, M. Benchohra, Measure of noncompactness and fractional hybrid differential equations with hybrid conditions, Differ. Equ. Appl. 14 (2022), 145-161, https://doi.org/10.7153/dea-2022-14-09Search in Google Scholar

[14] S. Dudek, Fixed point theorems in Fréchet algebras and Fréchet spaces and applications to nonlinear integral equations, Appl. Anal. Discrete Math. 11 (2017), 340-357.Search in Google Scholar

[15] K. J. Engel, R. Nagel, One-Parameter Semigroups for Linear Evolution Equations, Graduate Texts in Mathematics, 194, Springer-Verlag, New York, 2000.Search in Google Scholar

[16] M. Frigon, A. Granas, Résultats de type Leray-Schauder pour des contractions sur des espaces de Fréchet, Ann. Sci. Math. Québec 22 (2) (1998), 161-168.Search in Google Scholar

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

[18] E. Hernandez, On abstract differential equations with state dependent non-local conditions, J. Math. Anal. Appl. 466 (2018), 408-425.Search in Google Scholar

[19] E. Hernandez, D. O’Regan, On state dependent non-local conditions, Appl. Math. Lett. 83 (2018), 103-109.Search in Google Scholar

[20] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies 204, Elsevier, Amsterdam, 2006.Search in Google Scholar

[21] S. Krim, A. Salim, S. Abbas, 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/s12215-022-00818-8Search in Google Scholar

[22] V. Lakshmikantham, S. Leela, J. Vasundhara, Theory of Fractional Dynamic Systems, Cambridge Academic Publishers, Cambridge, 2009.Search in Google Scholar

[23] N. Laledj, A. Salim, J. E. Lazreg, S. Abbas, B. Ahmad, M. Benchohra, On implicit fractional q-difference equations: Analysis and stability. Math. Meth. Appl. Sci. (2022), 1-23, https://doi.org/10.1002/mma.8417Search in Google Scholar

[24] C. Lizama, Regularized solutions for abstract Volterra equations, J. Math. Anal. Appl. 243 (2000), 278-292.Search in Google Scholar

[25] H. Mönch, Boundary value problems for nonlinear ordinary differential equations of second order in Banach spaces, Nonlinear Anal. 4 (5) (1980), 985-999.Search in Google Scholar

[26] A. Ouahab, Local and global existence and uniqueness results for impulsive functional differential equations with multiple delay, J. Math. Anal. Appl. 323 (2006), 456-472.Search in Google Scholar

[27] A. Ouahab, Some uniqueness results for functional damped semilinear differential equations in Fréchet spaces, Acta Math. Sinica 24 (1) (2008), 95-106.Search in Google Scholar

[28] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, 1983.Search in Google Scholar

[29] J. Prüss, Evolutionary Integral Equations and Applications Monographs Math. 87, Bikhaüser Verlag, 1993.Search in Google Scholar

[30] A. Salim, M. Benchohra, J. R. Graef, J. E. Lazreg, Initial value problem for hybrid ψ-Hilfer fractional implicit differential equations, J. Fixed Point Theory Appl. 24 (2022), 14 pp., https://doi.org/10.1007/s11784-021-00920-xSearch in Google Scholar

[31] A. Salim, M. Benchohra, J. E. Lazreg and G. N’Guérékata, Existence and k-Mittag-Leffler-Ulam-Hyers stability results of k-generalized ψ-Hilfer boundary value problem, Nonlinear Stud. 29 (2022), 359-379.Search in Google Scholar

[32] A. Salim, J. E. Lazreg, B. Ahmad, M. Benchohra, J. J. Nieto, A study on k-generalized ψ-Hilfer derivative operator, Vietnam J. Math. (2022), https://doi.org/10.1007/s10013-022-00561-8Search in Google Scholar