HYERS-ULAM-RASSIAS STABILITY OF A NONLINEAR STOCHASTIC FRACTIONAL VOLTERRA INTEGRO-DIFFERENTIAL EQUATION

Reza Chaharpashlou; Antonio M. Lopes

doi:10.11948/20230005

2023 Volume 13 Issue 5

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Reza Chaharpashlou, Antonio M. Lopes. HYERS-ULAM-RASSIAS STABILITY OF A NONLINEAR STOCHASTIC FRACTIONAL VOLTERRA INTEGRO-DIFFERENTIAL EQUATION[J]. Journal of Applied Analysis & Computation, 2023, 13(5): 2799-2808. doi: 10.11948/20230005

Citation:

Reza Chaharpashlou, Antonio M. Lopes. HYERS-ULAM-RASSIAS STABILITY OF A NONLINEAR STOCHASTIC FRACTIONAL VOLTERRA INTEGRO-DIFFERENTIAL EQUATION[J]. Journal of Applied Analysis & Computation, 2023, 13(5): 2799-2808. doi: 10.11948/20230005

HYERS-ULAM-RASSIAS STABILITY OF A NONLINEAR STOCHASTIC FRACTIONAL VOLTERRA INTEGRO-DIFFERENTIAL EQUATION

Reza Chaharpashlou^1,,
Antonio M. Lopes^2, ,

1.
Department of Mathematics, Jundi-Shapur University of Technology, Dezful, Iran
2.
LAETA/INEGI, Faculty of Engineering, University of Porto, 4200-465 Porto, Portugal

Author Bio: Email: rchaharpashlou@gmail.com(R. Chaharpashlou)
Corresponding author: Email: aml@fe.up.pt (A. M. Lopes)

Abstract

Abstract

In this paper, we apply the fixed point technique to study the Hyers-Ulam and the Hyers-Ulam-Rassias stability of the stochastic fractional Volterra integro-differential equation with uncertainty for a kind of ϕ-Hilfer stochastic fractional differential equations. The findings represent an extension of some results found in the current literature.
- ϕ-Hilfer stochastic fractional derivative /
- Hyers-Ulam-Rassias stability /
- fixed point technique /
- stochastic fractional Volterra
MSC: 45Dxx, 58Cxx, 33Exx

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References

[1]	K. Biswas, G. Bohannan, R. Caponetto et al., Fractional-order devices, Springer, Cham, 2017. Google Scholar
[2]	R. Chaharpashlou and R. Saadati, Best approximation of a nonlinear fractional Volterra integro-differential equation in matrix MB-space, Advances in Difference Equations, 2021, 2021(1), 1–12. doi: 10.1186/s13662-020-03162-2 CrossRef Google Scholar
[3]	R. Chaharpashlou, R. Saadati and T. Abdeljawad, Existence, uniqueness and HUR stability of fractional integral equations by random matrix control functions in MMB-space, Journal of Taibah University for Science, 2021, 15(1), 574–578. doi: 10.1080/16583655.2021.1994787 CrossRef Google Scholar
[4]	R. Chaharpashlou, R. Saadati and A. Atangana, Ulam–Hyers–Rassias stability for nonlinear ψ-Hilfer stochastic fractional differential equation with uncertainty, Advances in Difference Equations, 2020, 2020(1), 1–10. doi: 10.1186/s13662-019-2438-0 CrossRef Google Scholar
[5]	R. Chaharpashlou, R. Saadati and A. M. Lopes, Fuzzy Mittag–Leffler–Hyers–Ulam–Rassias stability of stochastic differential equations, Mathematics, 2023, 11(9). Google Scholar
[6]	C. D. Constantinescu, J. M. Ramirez and W. R. Zhu, An application of fractional differential equations to risk theory, Finance and Stochastics, 2019, 23(4), 1001–1024. doi: 10.1007/s00780-019-00400-8 CrossRef Google Scholar
[7]	J. Diaz and B. Margolis, A fixed point theorem of the alternative, for contractions on a generalized complete metric space, in Amer. Math. Soc, 74, 1968, 305–309. Google Scholar
[8]	M. El-Moneam, T. F. Ibrahim and S. Elamody, Stability of a fractional difference equation of high order, J. Nonlinear Sci. Appl, 2019, 12(2), 65–74. Google Scholar
[9]	J. Jiang, D. O'Regan, J. Xu and Z. Fu, Positive solutions for a system of nonlinear Hadamard fractional differential equations involving coupled integral boundary conditions, Journal of Inequalities and Applications, 2019, 2019(1), 1–18. doi: 10.1186/s13660-019-1955-4 CrossRef Google Scholar
[10]	P. Li, L. Chen, R. Wu et al., Robust asymptotic stability of interval fractional-order nonlinear systems with time-delay, Journal of the Franklin Institute, 2018, 355(15), 7749–7763. doi: 10.1016/j.jfranklin.2018.08.017 CrossRef Google Scholar
[11]	A. M. Lopes and L. Chen, Fractional order systems and their applications, Fractal and Fractional, 2022, 6(7), 389. doi: 10.3390/fractalfract6070389 CrossRef Google Scholar
[12]	S. Sevgin and H. Sevli, Stability of a nonlinear Volterra integro-differential equation via a fixed point approach, J. Nonlinear Sci. Appl, 2016, 9(1), 200–207. doi: 10.22436/jnsa.009.01.18 CrossRef Google Scholar
[13]	J. Shu and J. Zhang, Random attractors for non-autonomous fractional stochastic Ginzburg-Landau equations on unbounded domains, Journal of Applied Analysis & Computation, 2020, 10(6), 2592–2618. Google Scholar
[14]	J. Sousa and E. C. de Oliveira, On the Ulam–Hyers–Rassias stability for nonlinear fractional differential equations using the ψ-Hilfer operator, Journal of Fixed Point Theory and Applications, 2018, 20(3), 1–21. Google Scholar
[15]	J. V. d. C. Sousa and E. C. De Oliveira, On the ψ-Hilfer fractional derivative, Communications in Nonlinear Science and Numerical Simulation, 2018, 60, 72–91. doi: 10.1016/j.cnsns.2018.01.005 CrossRef Google Scholar
[16]	H. Waheed, A. Zada and J. Xu, Well-posedness and Hyers-Ulam results for a class of impulsive fractional evolution equations, Mathematical Methods in the Applied Sciences, 2021, 44(1), 749–771. doi: 10.1002/mma.6784 CrossRef Google Scholar
[17]	J. Wang, M. Fec, Y. Zhou et al., Ulam's type stability of impulsive ordinary differential equations, Journal of Mathematical Analysis and Applications, 2012, 395(1), 258–264. doi: 10.1016/j.jmaa.2012.05.040 CrossRef Google Scholar
[18]	J. Wang and X. Li, A uniform method to Ulam–Hyers stability for some linear fractional equations, Mediterranean Journal of Mathematics, 2016, 13(2), 625–635. doi: 10.1007/s00009-015-0523-5 CrossRef Google Scholar
[19]	W. Wei, X. Li and X. Li, New stability results for fractional integral equation, Computers & Mathematics with Applications, 2012, 64(10), 3468–3476. Google Scholar
[20]	J. Xu, B. Pervaiz, A. Zada and S. O. Shah, Stability analysis of causal integral evolution impulsive systems on time scales, Acta Mathematica Scientia, 2021, 41(3), 781–800. doi: 10.1007/s10473-021-0310-2 CrossRef Google Scholar
[21]	J. Xu, Z. Wei, D. O'Regan and Y. Cui, Infinitely many solutions for fractional Schrödinger-Maxwell equations, Journal of Applied Analysis and Computation, 2019, 9(3), 1165–1182. Google Scholar