Optimal control problem for higher-order non-instantaneous impulsive fractional system with non-local conditions

References

• Balder, E. J. (1987). Necessary and sufficient conditions for L1-strong-weak lower semicontinuity of integral functionals. Nonlinear Analysis, 11(12), 1399–1404. https://doi.org/10.1016/0362-546X(87)90092-7
   Web of Science ®Google Scholar
• Byszewski, L., & Akca, H. (1997). On a mild solution of a semilinear functional-differential evolution nonlocal problem. Journal of Applied Mathematics and Stochastic Analysis, 10(3), 265–271. https://doi.org/10.1155/S1048953397000336
   Google Scholar
• Chalishajar, D., Kasinathan, R., Kasinathan, R., Kasinathan, D., & David, J. A. (2023a). Trajectory controllability of neutral stochastic integrodifferential equations with mixed fractional Brownian motion. Journal of Control and Decision, 1–15. https://doi.org/10.1080/23307706.2023.2271899
   Google Scholar
• Chalishajar, D., Ramkumar, K., Ravikumar, K., & Varshini, S. (2023b). Trajectory controllability of Hilfer fractional neutral stochastic differential equations with deviated argument using Rosenblatt process and Poisson jumps. Diferential Equations and Dynamical Systems, 1–22.
   Google Scholar
• Chang, Y. K., Pei, Y., & Ponce, R. (2019). Existence and optimal controls for fractional stochastic evolution equations of Sobolev type via fractional resolvent operators. Journal of Optimization Theory and Applications, 182(2), 558–572. https://doi.org/10.1007/s10957-018-1314-5
   Web of Science ®Google Scholar
• Da Prato, G., & Zabczyk, J. (2002). Second order partial differential equations in Hilbert spaces. Cambridge University Press.
   Google Scholar
• Dhayal, R., Malik, M., Abbas, S., & Debbouche, A. (2020). Optimal controls for second-order stochastic differential equations driven by mixed-fractional Brownian motion with impulses. Mathematical Methods in the Applied Sciences, 43(7), 4107–4124.
   Web of Science ®Google Scholar
• Granas, A., & Dugundji, J. (2003). Fixed point theory (Vol. 14, pp. 15–16). Springer.
   Google Scholar
• Guo, Y., Shu, X. B., Xu, F., & Yang, C. (2022). HJB equation for optimal control system with random impulses. Optimization, 1–25. https://doi.org/10.1080/02331934.2022.2154607
   Web of Science ®Google Scholar
• Hakkar, N., Dhayal, R., Debbouche, A., & Torres, D. F. (2023). Approximate controllability of delayed fractional stochastic differential systems with mixed noise and impulsive effects. Fractal and Fractional, 7(2), 104. https://doi.org/10.3390/fractalfract7020104
   Web of Science ®Google Scholar
• Huan, D. D., & Gao, H. (2015). Controllability of nonlocal second-order impulsive neutral stochastic functional integro-differential equations with delay and Poisson jumps. Cogent Engineering, 2(1), Article 1065585. https://doi.org/10.1080/23311916.2015.1065585
   Google Scholar
• Kilbas, A. A., Srivastava, H. M., & Trujillo, J. J. (2006). Theory and applications of fractional differential equations (Vol. 204). Elsevier.
   Google Scholar
• Kumar, A., Kumar, A., Vats, R. K., & Kumar, P. (2022). Approximate controllability of neutral delay integro-differential inclusion of order α∈(1,2) with non-instantaneous impulses. Evolution Equations and Control Theory, 11(5), 1635–1654. https://doi.org/10.3934/eect.2021058
   Google Scholar
• Lakshmikantham, V., Leela, S., & Vasundhara Devi, J. (2009). Theory of fractional dynamic systems. Cambridge Scientific Publishers.
   Google Scholar
• Malik, M., & Kumar, A. (2020). Existence and controllability results to second order neutral differential equation with non-instantaneous impulses. Journal of Control and Decision, 7(3), 286–308. https://doi.org/10.1080/23307706.2019.1571449
   Google Scholar
• Miller, K. S., & Ross, B. (1993). An introduction to the fractional calculus and fractional differential equations. John Willey.
   Google Scholar
• Mohan Raja, M., Vijayakumar, V., Shukla, A., Sooppy Nisar, K., Sakthivel, N., & Kaliraj, K. (2022). Optimal control and approximate controllability for fractional integrodifferential evolution equations with infinite delay of order r∈(1,2). Optimal Control Applications and Methods, 43(4), 996–1019. https://doi.org/10.1002/oca.v43.4
   Web of Science ®Google Scholar
• Patel, R., Shukla, A., & Jadon, S. S. (2022). Optimal control problem for fractional stochastic nonlocal semilinear system. Filomat, 36(4), 1381–1392. https://doi.org/10.2298/FIL2204381P
   Web of Science ®Google Scholar
• Pazy, A. (2012). Semigroups of linear operators and applications to partial differential equations (Vol. 44). Springer Science & Business Media.
   Google Scholar
• Samko, S. G., Kilbas, A. A., & Marichev, O. I. (1997). Fractional integrals and derivatives: Theory and applications. Gordon and Breach Science Publisher.
   Google Scholar
• Travis, C. C., & Webb, G. F. (1977). Compactness, regularity, and uniform continuity properties of strongly continuous cosine families. Houston Journal of Mathematics, 3(4), 555–567.
   Google Scholar
• Travis, C. C., & Webb, G. F. (1978a). Cosine families and abstract nonlinear second order differential equations. Acta Mathematica Academiae Scientiarum Hungarica, 32(1-2), 75–96. https://doi.org/10.1007/BF01902205
   Google Scholar
• Travis, C. C., & Webb, G. F. (1978b). Second order differential equations in Banach space. In Nonlinear equations in abstract spaces (pp. 331–361). Academic Press.
   Google Scholar