Significant findings for existence and controllability results of a class of nonlinear μ -Hilfer fractional evolution equations with time-varying delays
Source abstract
Abstract
In this research work, our primary focus is on exploring the existence and controllability aspects of a particular class of fractional evolution equations that incorporate time-varying delays. By means of some newly proposed criteria in combination with the generalized Grönwall inequality, novel outcomes have been derived. Eventually, a numerical illustration is presented to verify the correctness of the theoretical findings put forward.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Nonlinear Differential Equations Analysis · Fractional Differential Equations Solutions · Neural Networks Stability and Synchronization
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
General Education Center, Changsha Social Work College 1 , Changsha,
Department of Mathematics, Guizhou University 2 , Guiyang,
References (32)
Show source-provided references
1. 2006
2. 1999
3. Finite-time adaptive synchronization of fractional-order delayed quaternion-valued fuzzy neural networks
4. Adaptive synchronization of fractional-order uncertain complex-valued competitive neural networks under the non-decomposition method10.3390/fractalfract8080449 ↗
5. Approximate controllability of fractional neutral stochastic evolution equations in Hilbert spaces with fractional Brownian motion10.1080/07362994.2017.1386570 ↗
6. Existence of solutions and approximate controllability of fractional nonlocal stochastic differential equations of order 1 < q ≤ 2 with infinite delay and Poisson jumps10.1007/s12591-016-0340-8 ↗
7. Controllability of stochastic impulsive neutral functional differential equations driven by fractional Brownian motion with infinite delay10.1007/s12591-017-0401-7 ↗
8. On the approximate controllability for Hilfer fractional evolution hemivariational inequalities10.1080/01630563.2018.1499667 ↗
9. On the approximate controllability for fractional evolution inclusions of Sobolev and Clarke subdifferential type10.1093/imamci/dnx031 ↗
10. Relative controllability in fractional differential equations with pure delay10.1002/mma.4651 ↗
11. Controllability of fractional evolution inclusions with noninstantaneous impulses10.1515/ijnsns-2017-0090 ↗
12. Controllability of fractional non-instantaneous impulsive differential inclusions without compactness10.1093/imamci/dnx055 ↗
13. Approximate controllability of fractional stochastic differential inclusions with nonlocal conditions10.1080/00036811.2015.1090562 ↗
14. Approximate controllability of fractional nonlinear neutral stochastic differential inclusion with nonlocal conditions and infinite delay10.1007/s40065-017-0163-7 ↗
15. Approximate controllability results for fractional semilinear integro-differential inclusions in Hilbert spaces10.1007/s00025-016-0621-0 ↗
16. Approximate controllability of semilinear Hilfer fractional differential inclusions with impulsive control inclusion conditions in Banach spaces10.1016/j.chaos.2017.03.023 ↗
17. Relative controllability for conformable impulsive delay differential equations10.1093/imamci/dnae013 ↗
18. Relative controllability and Hyers–Ulam stability of Riemann–Liouville fractional delay differential System10.1007/s12346-024-01046-4 ↗
19. Relatively exact controllability of fractional stochastic neutral system with two incommensurate constant delays10.1002/mma.9932 ↗
20. Relatively exact controllability of fractional stochastic delay system driven by Lévy noise10.1002/mma.9175 ↗
21. Controllability of time-dependent neutral stochastic functional differential equations driven by a fractional Brownian motion10.22436/jnsa.011.06.11 ↗
22. Approximate controllability of impulse fractional stochastic integro-differential systems with state-dependent delay and Poisson jumps
23. On the ψ-Hilfer fractional derivative10.1016/j.cnsns.2018.01.005 ↗
24. Boundary controllability of nonlinear stochastic fractional systems in Hilbert spaces10.2478/amcs-2018-0009 ↗
25. Finite-time stability of a class of nonlinear fractional delay difference systems10.1016/j.aml.2019.06.017 ↗
26. 2014
27. On the Ulam–Hyers–Rassias stability for nonlinear fractional differential equations using the ψ-Hilfer operator10.1007/s11784-018-0587-5 ↗
28. Ulam–Hyers stability of a nonlinear fractional Volterra integro-differential equation10.1016/j.aml.2018.01.016 ↗
29. Existence of mild solutions for fractional integrodifferential equations of Sobolev type with nonlocal conditions10.1016/j.jmaa.2012.02.057 ↗
30. Existence results for an impulsive neutral integro-differential equation with infinite delay via fractional operators10.26637/mjm203/004 ↗
31. Fractional-order boundary value problems with Katugampola fractional integral conditions10.1186/s13662-018-1538-6 ↗
32. Fractional integral inequalities for continuous random variables10.26637/mjm202/010 ↗