Page 182 - IJOCTA-15-2

An investigation on the optimality condition of Caputo fractional time delay system
systems with both Dirichlet and Neumann con- 7. Sene N, Ndiaye A. Existence and uniqueness
ditions. Eventually, numerical example is worked study for partial neutral functional fractional dif-
out to validate the established results. These re- ferential equation under Caputo derivative. Int J
sults can be extended to a wider class of fractional Optimiz Control, 202414(3), 208-219.
delay differential systems with suitable modifica- https://doi.org/10.11121/ijocta.1464
tions.
¨
8. Evirgen F, U¸car S, Ozdemir N, Jajarmi A. En-
Acknowledgments hancing maize foliar disease management through
fractional optimal control strategies. Discrete
The author expresses sincere gratitude to Mahin-
Contin Dynam Syst-S, 2025;18(5): 1353-1371.
dra University for supporting this research.
https://doi.org/10.3934/dcdss.2024150
Funding
9. Baleanu D, Jajarmi A, Sajjadi SS, Mozyrska D.
This work has financial support of Farhangian
A new fractional model and optimal control of a
University (Contract No. 500.17474.120).
tumor immune surveillance with non-singular de-
rivative operator. Chaos.2019; 29(8): 083127.
Conflict of interest
https://doi.org/10.1063/1.5096159
The author declare that they have no conflict of
interest regarding the publication of this article. 10. Baleanu D, Hajipour M, Jajarmi A. An accurate
finite difference formula for the numerical solu-
Author contributions
tion of delay-dependent fractional optimal con-
This is a single-authored article. trol problems. Int J OptimizContr Theor Appl.,
2024;14(3):183-192.
Availability of data https://doi.org/10.11121/ijocta.1478

Not applicable.
11. Sarkar D,, Chandok S, Konar P, Bhardwaj R,
References Choudhary PRS. Coupling, optimization and the
effect of binary relation. J Anal., 2023;31, 1081-
1. Barbu V. Hamilton-Jacobi equations and non- 1100.
linear control problems. J Math Anal Appl., https://doi.org/10.1007/s41478-022-00503-0
1986;120:494-509.
https://doi.org/10.1016/0022-247X(86)90171-X
12. Sahijwani L, Sukavanam N. Approximate control-
2. Barron EN, Jensen R. The Pontryagin maximum lability for Riemann-Liouville fractional differen-
princple from dynamic programming and vis- tial equations. Int J Optimiz Control: Theo-
cosity solutions to first order partial differential rAppl. 2023;13:59-67.
equations. Trans Am MathSoc. 1986; 298:635- https://doi.org/10.11121/ijocta.2023.1178
641.
https://doi.org/10.1090/S0002-9947-1986-
13. Durga N, Muthukumar P. Optimal control of frac-
0860384-4
tional reaction-diffusion equations with Poisson
3. Pontryagin LS. The Mathematical Theory of Op- jumps. J Anal., 2019;27:605-621.
timal Processes. New York:Interscience;1962. https://doi.org/10.1007/s41478-018-0097-2
4. Jajarmi A, Baleanu D. On the fractional optimal
control problems with a general derivative opera- 14. Bahaa GM. Fractional optimal control prob-
tor. Asian J Control. 2021;23(2):1062-1071. lem for variational inequalities with control
https://doi.org/10.1002/asjc.2282 constraints. IMA J Math Control Inform.,
2018;35(1): 107-122.
5. Razminia A, Asadizadehshiraz M, Torres DFM.
Fractional order version of the Hamilton-Jacobi-
15. Lions JL. Optimal Control of Systems Gov-
Bellman equation. J Comput Nonlinear Dyn.
erned by Partial Differential Equations. Band 170.
2019;14(1): 011005.
Berlin:Springer; 1971.
https://doi.org/10.1115/1.4041912
https://doi.org/10.1007/978-3-642-65024-6
6. Haq A, Sukavanam N. Controllability of nonlin-
ear fractional integrodifferential systems involving
16. Pazy A. Semigroups of Linear Operators and Ap-
multiple delays in control. Int J OptimizControl
plications to Partial Differential Equations. New
Theor Appl. 2024;14(1):1-11.
York/Berlin/Heidelberg:Springer-Verlag; 1983.
https://doi.org/10.11121/ijocta.1428
https://doi.org/10.1007/978-1-4612-5561-1
377