Existence and controllability of stochastic fractional semilinear inclusion problem with weighted time delay

Li Xin Gong; Yong Zhou

Ayuda

Existence and controllability of stochastic fractional semilinear inclusion problem with weighted time delay

Li Xin Gong ^[1] ; Yong Zhou ^[2]
1. [1] Guizhou University
  
  Guizhou University
  
  China
2. [2] Macau University of Science and Technology
  
  Macau University of Science and Technology
  
  RAE de Macao (China)
Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 25, Nº 1, 2026
Idioma: inglés
Enlaces
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Resumen
- In this paper, we investigate the existence and controllability of stochastic fractional semilinear differential inclusions with weighted time delay by using stochastic analysis, fractional calculus theory and the fixed point theorem. On the basis of studying the non-emptiness and compactness of mild solution sets, we prove the theorems that guarantee the complete controllability of the system under consideration.
Referencias bibliográficas
- 1. Agarwal, R.P., Belmekki, M., Benchohra, M.: A survey on semilinear differential equations and inclusions involving Riemann-Liouville fractional...
- 2. Ahmed, N.U.: Dynamic Systems and Control with Applications. World Scientic, Singapore (2006)
- 3. Ahmed, H.M., El-Owaidy, H.M., AL-Nahhas, M.A.: Neutral fractional stochastic partial differential equations with Clarke subdifferential....
- 4. Bashirov, A.E., Mahmudov, N.I.: On concepts of controllability for deterministic and stochastic systems. SIAM J. Control. Optim. 37(6),...
- 5. Cheng, Y., Agarwal, R.P., O’Regan, D.: Existence and controllability for nonlinear fractional differential inclusions with nonlocal boundary...
- 6. Da Prato, G., Zabczyk, J.: Stochastic equations in infinite dimensions, Cambridge university press, (2014)
- 7. Dineshkumar, C., Udhayakumar, R., Vijayakumar, V., et al.: A note on approximate controllability for nonlocal fractional evolution stochastic...
- 8. Dineshkumar, C., Udhayakumar, R., Vijayakumar, V., et al.: A note concerning to approximate controllability of Atangana-Baleanu fractional...
- 9. Dineshkumar, C., Nisar, K.S., Udhayakumar, R., et al.: New discussion about the approximate controllability of fractional stochastic differential...
- 10. Fu, X.: Controllability of non-densely defined functional differential systems in abstract space. Appl. Math. Lett. 19(4), 369–377 (2006)
- 11. Hao, J.W., Li, M.M.: A new class of fractional Navier-Stokes system coupled with multivalued boundary conditions. Commun. Nonlinear Sci....
- 12. Hao, J.W., Wang, J.R., Lu, L.: Coupled system of fractional hemivariational inequalities with applications. Optimization 73, 969–994 (2024)
- 13. He, J.W., Peng, L.: Approximate controllability for a class of fractional stochastic wave equations. Comput. Math. Appl. 78(5), 1463–1476...
- 14. Hu, S., Papageorgiou, N.S.: Handbook of Multivalued Analysis (Theory). Kluwer Academic Publishers, Dordrecht, Boston, London (1997)
- 15. Jeong, J.M., Son, S.J.: Time optimal control of semilinear control systems involving time delays. J. Optim. Theory Appl. 165(3), 793–811...
- 16. Kumar, S.: Mild solution and fractional optimal control of semilinear system with fixed delay. J. Optim. Theory Appl. 174(1), 108–121...
- 17. Le Gall, J.-F.: Brownian Motion, Martingales, and Stochastic Calculus, Springer International Publishing, (2016)
- 18. Li, K.X., Peng, J.G., Jia, J.X.: Cauchy problems for fractional differential equations with RiemannLiouville fractional derivatives. J....
- 19. Ma, T.W.: Topological degrees for set-valued compact vector fields in locally convex spaces. Dissertationess Math 92, 1–43 (1972)
- 20. Migórski, S., Ochal, A., Sofonea, M.: Nonlinear Inclusions and Hemivariational Inequalities, Models and Analysis of Contact Problems,...
- 21. Migórski, S., Ochal, A.: Quasi-static hemivariational inequality via vanishing acceleration approach. SIAM J. Math. Anal 41(4), 1415–1435...
- 22. Mishra, K.K., Dubey, S., Baleanu, D.: Existence and controllability of a class of non-autonomous nonlinear evolution fractional integrodifferential...
- 23. Raja, M.M., Vijayakumar, V., Udhayakumar, R., et al.: A new approach on the approximate controllability of fractional differential evolution...
- 24. Sakthivel, R., Suganya, S., Anthoni, S.M.: Approximate controllability of fractional stochastic evolution equations. Computers Mathematics...
- 25. Sakthivel, R., Ganesh, R., Anthoni, S.M.: Approximate controllability of fractional nonlinear differential inclusions. Appl. Math. Comput....
- 26. Selvam, A.P., Vellappandi, M., Govindaraj, V.: Controllability of fractional dynamical systems with -Caputo fractional derivative. Phys....
- 27. Travis, C.C., Webb, G.F.: Compactness, regularity, and uniform continuity properties of strongly continuous cosine families. Houst. J....
- 28. Wang, J.R., Zhou, Y.: Existence and controllability results for fractional semilinear differential inclusions. Nonlinear Anal. Real World...
- 29. Wang, J.R., Zhou, Y.: Complete controllability of fractional evolution systems. Commun. Nonlinear Sci. Numer. Simul. 17(11), 4346–4355...
- 30. Wang, J.R., Zhou, Y., Medved, M.: On the solvability and optimal controls of fractional integrodifferential evolution systems with infinite...
- 31. Williams, W.K., Vijayakumar, V., Udhayakumar, R., et al.: A new study on existence and uniqueness of nonlocal fractional delay differential...
- 32. Yang, H.: Existence and approximate controllability of Riemann-Liouville fractional evolution equations of order 1 μ 2 with weighted time...
- 33. Ye, H.P., Gao, J.M., Ding, Y.H.: A generalized Gronwall inequality and its application to a fractional differential equation. J. Math....
- 34. Zhou, Y.: Basic Theory of Fractional Differential Equations. World Scientific, Singapore (2014)
- 35. Zhou, Y., Peng, L.: Topological properties of solutions sets for partial functional evolution inclusions. C.R. Math. 355, 45–64 (2017)
- 36. Zhou, Y., Wang, R.N., Peng, L.: Topological Structure of the Solution Set for Evolution Inclusions. Springer, Singapore (2017)
- 37. Zhu, S.G., Fan, Z.B., Li, G.: Optimal controls for Riemann-Liouville fractional evolution systems without Lipschitz assumption. J. Optim....
- 38. Zhu, S.G., Fan, Z.B., Li, G.: Topological characteristics of solution sets for fractional evolution equations and applications to control...