Abstract
In this paper, we consider a coupled system of fractional stochastic differential equations involving the Hilfer derivative of order
References
[1] S. Abbas, B. Ahmad, M. Benchohra and A. Salim, Fractional Difference, Differential Equations, and Inclusions: Analysis and Stability, Elsevier, Amsterdam, 2024. Search in Google Scholar
[2] R. Agarwal, S. Hristova and D. O’Regan, Non-instantaneous impulses in Caputo fractional differential equations, Fract. Calc. Appl. Anal. 20 (2017), no. 3, 595–622. 10.1515/fca-2017-0032Search in Google Scholar
[3] R. Agarwal, S. Hristova and D. O’Regan, Existence and integral representation of scalar Riemann–Liouville fractional differential equations with delay and impulses, Mathematics 8 (2020), 10.3390/math8040607. 10.3390/math8040607Search in Google Scholar
[4] H. M. Ahmed and M. M. El-Borai, Hilfer fractional stochastic integro-differential equations, Appl. Math. Comput. 331 (2018), 182–189. 10.1016/j.amc.2018.03.009Search in Google Scholar
[5] H. M. Ahmed, M. M. El-Borai and M. E. Ramadan, Noninstantaneous impulsive and nonlocal Hilfer fractional stochastic integrodifferential equations with fractional Brownian motion and Poisson jumps, Int. J. Nonlinear Sci. Numer. Simul. 22 (2021), no. 7–8, 927–942. 10.1515/ijnsns-2019-0274Search in Google Scholar
[6] F. Z. Arioui, Weighted fractional stochastic integro-differential equation with infinite delay, Arab. J. Math. 12 (2023), no. 3, 499–511. 10.1007/s40065-023-00430-3Search in Google Scholar
[7]
A. Boutiara, J. Alzabut, M. Ghaderi and S. Rezapour,
On a coupled system of fractional
[8]
R. Chaudhary, M. Muslim and D. N. Pandey,
Approximation of solutions to fractional stochastic integro-differential equations of order
[9] G. Da Prato and J. Zabczyk, Stochastic Equations in Infinite Dimensions, Encyclopedia Math. Appl. 44, Cambridge University, Cambridge, 1992. 10.1017/CBO9780511666223Search in Google Scholar
[10] K. Dhawan, R. K. Vats and R. P. Agarwal, Qualitative analysis of coupled fractional differential equations involving Hilfer derivative, An. Ştiinţ. Univ. “Ovidius” Constanţa Ser. Mat. 30 (2022), no. 1, 191–217. 10.2478/auom-2022-0011Search in Google Scholar
[11] K. Diethelm, The Analysis of Fractional Differential Equations, Lecture Notes in Math. 2004, Springer, Berlin, 2010. 10.1007/978-3-642-14574-2Search in Google Scholar
[12] J. Du, W. Jiang and A. U. K. Niazi, Approximate controllability of impulsive Hilfer fractional differential inclusions, J. Nonlinear Sci. Appl. 10 (2017), no. 2, 595–611. 10.22436/jnsa.010.02.23Search in Google Scholar
[13] L. C. Evans, Partial Differential Equations, Grad. Stud. Math. 19, American Mathematical Society, Providence, 1998. Search in Google Scholar
[14] K. M. Furati, M. D. Kassim and N. Tatar, Existence and uniqueness for a problem involving Hilfer fractional derivative, Comput. Math. Appl. 64 (2012), no. 6, 1616–1626. 10.1016/j.camwa.2012.01.009Search in Google Scholar
[15] H. Gou, Y. Li and Q. Li, Mixed monotone iterative technique for Hilfer fractional evolution equations with nonlocal conditions, J. Appl. Anal. Comput. 10 (2020), no. 5, 1823–1847. 10.11948/20190211Search in Google Scholar
[16] H. Gu and J. J. Trujillo, Existence of mild solution for evolution equation with Hilfer fractional derivative, Appl. Math. Comput. 257 (2015), 344–354. 10.1016/j.amc.2014.10.083Search in Google Scholar
[17] R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific, River Edge, 2000. 10.1142/9789812817747Search in Google Scholar
[18] R. Hilfer, Y. Luchko and Ž. Tomovski, Operational method for the solution of fractional differential equations with generalized Riemann–Liouville fractional derivatives, Fract. Calc. Appl. Anal. 12 (2009), no. 3, 299–318. Search in Google Scholar
[19] P. Kalamani, D. Baleanu, S. Selvarasu and M. M. Arjunan, On existence results for impulsive fractional neutral stochastic integro-differential equations with nonlocal and state-dependent delay conditions, Adv. Difference Equ. 2016 (2016), Paper No. 163. 10.1186/s13662-016-0885-4Search in Google Scholar
[20] R. Kamocki, A new representation formula for the Hilfer fractional derivative and its application, J. Comput. Appl. Math. 308 (2016), 39–45. 10.1016/j.cam.2016.05.014Search in Google Scholar
[21] A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Math. Stud. 204, Elsevier Science, Amsterdam, 2006. Search in Google Scholar
[22] J. Lv and X. Yang, A class of Hilfer fractional stochastic differential equations and optimal controls, Adv. Difference Equ. 2019 (2019), Paper No. 17. 10.1186/s13662-019-1953-3Search in Google Scholar
[23] A. I. Perov, On the Cauchy problem for a system of ordinary differential equations, Približ. Metod. Rešen. Differ. Uravnen. (1964), no. 2, 115–134. Search in Google Scholar
[24] I. Podlubny, Fractional Differential Equations, Math. Sci. Eng. 198, Academic Press, San Diego, 1999. Search in Google Scholar
[25] Y. Qin, Analytic Inequalities and Their Applications in PDEs, Oper. Theory Adv. Appl. 241, Birkhäuser/Springer, Cham, 2017. 10.1007/978-3-319-00831-8Search in Google Scholar
[26] S. Sivasankar, R. Udhayakumar, M. Hari Kishor, S. Alhazmi and S. Al-Omari, A new result concerning nonlocal controllability of Hilfer fractional stochastic differential equations via almost sectorial operators, Mathematics 11 (2023), 10.3390/math11010159. 10.3390/math11010159Search in Google Scholar
[27] S. Sivasankar, R. Udhayakumar, V. Subramanian, G. AlNemer and A. Elshenhab, Existence of Hilfer fractional stochastic differential equations with nonlocal conditions and delay via almost sectorial operators, Mathematics 10 (2022), 10.3390/math10224392. 10.3390/math10224392Search in Google Scholar
[28] H. A. Wahash, M. S. Abdo, S. K. Panchal and S. P. Bhairat, Existence of solution for Hilfer fractional differential problem with nonlocal boundary condition in Banach spaces, Stud. Univ. Babeş-Bolyai Math. 66 (2021), no. 3, 521–536. 10.24193/subbmath.2021.3.09Search in Google Scholar
[29] J. Wang, A. G. Ibrahim and D. O’Regan, Finite approximate controllability of Hilfer fractional semilinear differential equations, Miskolc Math. Notes 21 (2020), no. 1, 489–507. 10.18514/MMN.2020.2921Search in Google Scholar
© 2024 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Existence results for a coupled system of fractional stochastic differential equations involving Hilfer derivative
- Minimax interpolation of continuous time stochastic processes with periodically correlated increments observed with noise
- On optimal control of coupled mean-field forward-backward stochastic equations
- Double sequences of complex uncertain variables associated with multiplier sequences
- The estimator G 59 for the solutions of the regularized Kolmogorov--Wiener filter
- Canonical equation K 107 for symmetric matrix with independent zebra random lines
- Existence of a weak solution to a Markovian BSDE with discontinuous coefficients
- Generalized delay BSDE driven by fractional Brownian motion
- Stochastic integration respect a cylindrical martingale-Lévy process with second moments
Articles in the same Issue
- Frontmatter
- Existence results for a coupled system of fractional stochastic differential equations involving Hilfer derivative
- Minimax interpolation of continuous time stochastic processes with periodically correlated increments observed with noise
- On optimal control of coupled mean-field forward-backward stochastic equations
- Double sequences of complex uncertain variables associated with multiplier sequences
- The estimator G 59 for the solutions of the regularized Kolmogorov--Wiener filter
- Canonical equation K 107 for symmetric matrix with independent zebra random lines
- Existence of a weak solution to a Markovian BSDE with discontinuous coefficients
- Generalized delay BSDE driven by fractional Brownian motion
- Stochastic integration respect a cylindrical martingale-Lévy process with second moments