On Ulam type of stability for stochastic integral equations with Volterra noise

References

[1] M. S. Abdo, A. M. Saeed, H. A. Wahash and S. K. Panchal, On nonlocal problems for fractional integro-differential equation in Banach space, European J. Sci. Res. 151 (2019), 320–334. Suche in Google Scholar

[2] A. Ali, K. Shah and D. Baleanu, Ulam stability results to a class of nonlinear implicit boundary value problems of impulsive fractional differential equations, Adv. Difference Equ. 2019 (2019), Paper No. 5. 10.1186/s13662-018-1940-0Suche in Google Scholar

[3] S. András and J. J. Kolumbán, On the Ulam Hyers stability of first order differential systems with nonlocal initial conditions, Nonlinear Anal. 82 (2013), 1–11. 10.1016/j.na.2012.12.008Suche in Google Scholar

[4] G. Arthi, J. H. Park and H. Y. Jung, Existence and controllability results for second-order impulsive stochastic evolution systems with state-dependent delay, Appl. Math. Comput. 248 (2014), 328–341. 10.1016/j.amc.2014.09.084Suche in Google Scholar

[5] P. W. Bates, On some nonlocal evolution equations arising in materials science, Nonlinear Dynamics and Evolution Equations, Fields Inst. Commun. 48, American Mathematical Society, Providence (2006), 13–52. 10.1090/fic/048/02Suche in Google Scholar

[6] S. A. Bishop and E. O. Ayoola, Existence and uniqueness of solutions of a class of quantum stochastic evolution equations, J. Math. Extension 15 (2021), no. 2, 1–14. Suche in Google Scholar

[7] S. A. Bishop, K. S. Eke and H. I. Okagbue, Advances on asymptotic stability of impulsive stochastic evolution equations, Int. J. Math. Comput. Sci. 16 (2021), no. 1, 99–109. Suche in Google Scholar

[8] S. A. Bishop, S. A. Iyase and H. I. Okagbue, Stability of well-posed stochastic evolution equation, Heliyon 5 (2019), no. 11, Article ID e02832. 10.1016/j.heliyon.2019.e02832Suche in Google Scholar PubMed PubMed Central

[9] S. A. Bishop and A. C. Nnubia, Stability of nonlocal stochastic Volterra equations, Int. J. Math. Anal. Optim. 7 (2021), no. 2, 48–55. 10.52968/28302767Suche in Google Scholar

[10] S. A. Bishop, G. A. Okeke and K. Eke, Mild solutions of evolution quantum stochastic differential equations with nonlocal conditions, Math. Methods Appl. Sci. 43 (2020), no. 10, 6254–6261. 10.1002/mma.6368Suche in Google Scholar

[11] L. Byszewski, Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem, J. Math. Anal. Appl. 162 (1991), no. 2, 494–505. 10.1016/0022-247X(91)90164-USuche in Google Scholar

[12] L. P. Castro and A. M. Simões, Hyers–Ulam–Rassias stability of nonlinear integral equations through the Bielecki metric, Math. Methods Appl. Sci. 41 (2018), no. 17, 7367–7383. 10.1002/mma.4857Suche in Google Scholar

[13] P. Čoupek and B. Maslowski, Stochastic evolution equations with Volterra noise, Stochastic Process. Appl. 127 (2017), no. 3, 877–900. 10.1016/j.spa.2016.07.003Suche in Google Scholar

[14] K. D. Kucche and P. U. Shikhare, Ulam–Hyers stability of integrodifferential equations in Banach spaces via Pachpatte’s inequality, Asian-Eur. J. Math. 11 (2018), no. 4, Article ID 1850062. 10.1142/S1793557118500626Suche in Google Scholar

[15] K. D. Kucche and P. U. Shikhare, Ulam stabilities for nonlinear Volterra delay integro-differential equations, Int. J. Nonlinear Anal. Appl. 9 (2018), no. 2, 145–159. Suche in Google Scholar

[16] K. D. Kucche and P. U. Shikhare, Ulam stabilities via Pachpatte’s inequality for Volterra–Fredholm delay integrodifferential equations in Banach spaces, Note Mat. 38 (2018), no. 1, 67–82. Suche in Google Scholar

[17] X. Li, W. Jiang and J. Xiang, Existence and Hyers–Ulam stability results for nonlinear fractional systems with coupled nonlocal initial conditions, J. Appl. Math. Comput. 50 (2016), no. 1–2, 493–509. 10.1007/s12190-015-0881-ySuche in Google Scholar

[18] Z. Liu and R. Wang, A note on fractional equations of Volterra type with nonlocal boundary condition, Abstr. Appl. Anal. 2013 (2013), Article ID 432941. 10.1155/2013/432941Suche in Google Scholar

[19] R. H. Martin, Jr., Nonlinear Operators and Differential Equations in Banach Spaces, Pure Appl. Math., Wiley-Interscience, New York, 1976. Suche in Google Scholar

[20] N. P. N. Ngoc, Ulam–Hyers–Rassias stability of a nonlinear stochastic integral equation of Volterra type, Differ. Equ. Appl. 9 (2017), no. 2, 183–193. 10.7153/dea-09-15Suche in Google Scholar

[21] S. K. Ntouyas and P. C. Tsamatos, Global existence for semilinear evolution equations with nonlocal conditions, J. Math. Anal. Appl. 210 (1997), no. 2, 679–687. 10.1006/jmaa.1997.5425Suche in Google Scholar

[22] A. Vinodkumar, Existence, uniqueness and stability results of impulsive stochastic semilinear functional differential equations with infinite delays, J. Nonlinear Sci. Appl. 4 (2011), no. 4, 236–246. 10.22436/jnsa.004.04.02Suche in Google Scholar

[23] J. A. Walker, Dynamical Systems and Evolution Equations, Math. Concepts Methods Sci. Eng. 20, Plenum, New York, 1980. 10.1007/978-1-4684-1036-5_3Suche in Google Scholar

[24] J. Wang, K. Shah and A. Ali, Existence and Hyers–Ulam stability of fractional nonlinear impulsive switched coupled evolution equations, Math. Methods Appl. Sci. 41 (2018), no. 6, 2392–2402. 10.1002/mma.4748Suche in Google Scholar

[25] A. Zada, U. Riaz and F. U. Khan, Hyers–Ulam stability of impulsive integral equations, Boll. Unione Mat. Ital. 12 (2019), no. 3, 453–467. 10.1007/s40574-018-0180-2Suche in Google Scholar

[26] L. Zhu, Q. Huang and G. Li, Existence and asymptotic properties of solutions of nonlinear multivalued differential inclusions with nonlocal conditions, J. Math. Anal. Appl. 390 (2012), no. 2, 523–534. 10.1016/j.jmaa.2012.01.055Suche in Google Scholar