A cardinal-based numerical method for fractional optimal control problems with Caputo–Katugampola fractional derivative in a large domain

References

• Aadhithiyan, S., Raja, R., Zhu, Q., Alzabut, J., Niezabitowski, M., & Lim, C. P. (2021). Modified projective synchronization of distributive fractional order complex dynamic networks with model uncertainty via adaptive control. Chaos, Solitons and Fractals, 147, 110853. https://doi.org/10.1016/j.chaos.2021.110853
   Web of Science ®Google Scholar
• Abdelhakem, M., Moussa, H., Baleanu, D., & El-Kady, M. (2019). Shifted Chebyshev schemes for solving fractional optimal control problems. Journal of Vibration and Control, 25(15), 2143–2150. https://doi.org/10.1177/1077546319852218
   Web of Science ®Google Scholar
• Agrawal, O. P. (2004). A general formulation and solution scheme for fractional optimal control problems. Nonlinear Dynamics, 38(1–4), 323–337. https://doi.org/10.1007/s11071-004-3764-6
   Web of Science ®Google Scholar
• Agrawal, O. P. (2008). A formulation and numerical scheme for fractional optimal control problems. Journal of Vibration and Control, 14(9–10), 1291–1299. https://doi.org/10.1177/1077546307087451
   Web of Science ®Google Scholar
• Almeida, R., Malinowska, A. B., & Odzijewicz, T. (2016). Fractional differential equations with dependence on the Caputo-Katugampola derivative. Journal of Computational and Nonlinear Dynamics, 11(6), 061017. https://doi.org/10.1115/1.4034432
   Web of Science ®Google Scholar
• Ben Makhlouf, A., & Nagy, A. M. (2020). Finite-time stability of linear Caputo-Katugampola fractional-order time delay systems. Asian Journal of Control, 22(1), 297–306. https://doi.org/10.1002/asjc.v22.1
   Web of Science ®Google Scholar
• Canuto, C., Hussaini, M., Quarteroni, A., & Zang, T. (1988). Spectral methods in fluid dynamics. Springer-Verlage.
   Google Scholar
• Dai, M., Jiang, Y., Du, J., & Tang, G. (2022). Finite time stability of Caputo-Katugampola fractional order time delay projection neural networks. Neural Processing Letters, 54(6), 4851–4867. https://doi.org/10.1007/s11063-022-10838-1
   Web of Science ®Google Scholar
• Erturk, V. S., & Kumar, P. (2020). Solution of a COVID-19 model via new generalized Caputo-type fractional derivatives. Chaos, Solitons and Fractals, 139, 110280. https://doi.org/10.1016/j.chaos.2020.110280
   PubMed Web of Science ®Google Scholar
• Gambo, Y. Y., Jarad, F., Baleanu, D., & Abdeljawad, T. (2014). On Caputo modification of the Hadamard fractional derivatives. Advances in Difference Equations, 2014(1), 1–12. https://doi.org/10.1186/1687-1847-2014-10
   Google Scholar
• Ghanbari, B., & Atangana, A. (2020). Some new edge detecting techniques based on fractional derivatives with non-local and non-singular kernels. Advances in Difference Equations, 2020(1), 1–19. https://doi.org/10.1186/s13662-019-2438-0
   PubMed Web of Science ®Google Scholar
• Ghosh, S. (2022). Numerical study on fractional-order Lotka-Volterra model with spectral method and Adams-Bashforth-Moulton method. International Journal of Applied and Computational Mathematics, 8(5), 233. https://doi.org/10.1007/s40819-022-01457-4
   Google Scholar
• Ghosh, S. (2024). An analytical approach for the fractional-order hepatitis b model using new operator. International Journal of Biomathematics, 17(01), 2350008. https://doi.org/10.1142/S1793524523500080
   Web of Science ®Google Scholar
• Gong, Z., Liu, C., Teo, K. L., Wang, S., & Wu, Y. (2021). Numerical solution of free final time fractional optimal control problems. Applied Mathematics and Computation, 405, 126270. https://doi.org/10.1016/j.amc.2021.126270
   Web of Science ®Google Scholar
• Hassani, H., Machado, T. J., Hosseini Asl, M. K., & Dahaghin, M. S. (2021). Numerical solution of nonlinear fractional optimal control problems using generalized Bernoulli polynomials. Optimal Control Applications and Methods, 42(4), 1045–1063. https://doi.org/10.1002/oca.v42.4
   Web of Science ®Google Scholar
• Heydari, M. H., Mahmoudi, M. R., Shakiba, A., & Avazzadeh, Z. (2018). Chebyshev cardinal wavelets and their application in solving nonlinear stochastic differential equations with fractional Brownian motion. Communications in Nonlinear Science and Numerical Simulation, 64, 98–121. https://doi.org/10.1016/j.cnsns.2018.04.018
   Web of Science ®Google Scholar
• Heydari, M. H., & Razzaghi, M. (2021). A numerical approach for a class of nonlinear optimal control problems with piecewise fractional derivative. Chaos, Solitons and Fractals, 152, 111465. https://doi.org/10.1016/j.chaos.2021.111465
   Web of Science ®Google Scholar
• Heydari, M. H., & Razzaghi, M. (2021). Piecewise Chebyshev cardinal functions: Application for constrained fractional optimal control problems. Chaos, Solitons and Fractals, 150, 111118. https://doi.org/10.1016/j.chaos.2021.111118
   Web of Science ®Google Scholar
• Heydari, M. H., & Razzaghi, M. (2022). A new class of orthonormal basis functions: Application for fractional optimal control problems. International Journal of Systems Science, 53(2), 240–252. https://doi.org/10.1080/00207721.2021.1947411
   Web of Science ®Google Scholar
• Jarad, F., Abdeljawad, T., & Baleanu, D. (2012). Caputo-type modification of the Hadamard fractional derivatives. Advances in Difference Equations, 2012, 1–8. https://doi.org/10.1186/1687-1847-2012-1
   Web of Science ®Google Scholar
• Kahouli, O., Jmal, A., Naifar, O., Nagy, A. M., & Ben Makhlouf, A. (2022). New result for the analysis of Katugampola fractional-order systems—application to identification problems. Mathematics, 10(11), 1814. https://doi.org/10.3390/math10111814
   Web of Science ®Google Scholar
• Karami, Sh., Fakharzadeh Jahromi, A., & Heydari, M. H. (2022). A computational method based on the generalized Lucas polynomials for fractional optimal control problems. Advances in Continuous and Discrete Models, 2022(1), 64. https://doi.org/10.1186/s13662-022-03737-1
   Google Scholar
• Katugampola, U. N. (2011). New approach to a generalized fractional integral. Applied Mathematics and Computation, 218(3), 860–865. https://doi.org/10.1016/j.amc.2011.03.062
   Web of Science ®Google Scholar
• Kilbas, A. A., Srivastava, H. M., & Trujillo, J. J. (2006). Theory and applications of fractional differential equations. Vol. 204, Elsevier.
   Google Scholar
• Li, M. (2020). Multi-fractional generalized Cauchy process and its application to teletraffic. Physica A: Statistical Mechanics and Its Applications, 550, 1–14.
   Web of Science ®Google Scholar
• Li, M. (2021). Modified multifractional Gaussian noise and its application. Physica Scripta, 96(12), 1–12.
   Web of Science ®Google Scholar
• Mamehrashi, K. (2023). Ritz approximate method for solving delay fractional optimal control problems. Journal of Computational and Applied Mathematics, 417, 114606. https://doi.org/10.1016/j.cam.2022.114606
   Web of Science ®Google Scholar
• Marzban, H. R. (2023). An accurate method for fractional optimal control problems governed by nonlinear multi-delay systems. Journal of Vibration and Control, 29(3–4), 820–843. https://doi.org/10.1177/10775463211053182
   Web of Science ®Google Scholar
• Phang, C., Ismail, N. F., Isah, A., & Loh, J. R. (2018). A new efficient numerical scheme for solving fractional optimal control problems via a Genocchi operational matrix of integration. Journal of Vibration and Control, 24(14), 3036–3048. https://doi.org/10.1177/1077546317698909
   Web of Science ®Google Scholar
• Pooseh, S., Almeida, R., & Torres, D. F. M. (2014). Fractional order optimal control problems with free terminal time. Journal of Industrial and Management Optimization, 10(2), 363–381. https://doi.org/10.3934/jimo.2014.10.363
   Web of Science ®Google Scholar
• Postavaru, O., & Toma, A. (2022). A numerical approach based on fractional-order hybrid functions of block-pulse and Bernoulli polynomials for numerical solutions of fractional optimal control problems. Mathematics and Computers in Simulation, 194, 269–284. https://doi.org/10.1016/j.matcom.2021.12.001
   Web of Science ®Google Scholar
• Rabiei, K., & Razzaghi, M. (2023). An approach to solve fractional optimal control problems via fractional-order Boubaker wavelets. Journal of Vibration and Control, 29(7–8), 1806–1819. https://doi.org/10.1177/10775463211070902
   Web of Science ®Google Scholar
• Redhwan, S. S., Shaikh, S. L., & Abdo, M. S. (2022). Caputo-Katugampola-type implicit fractional differential equation with anti-periodic boundary conditions. Results in Nonlinear Analysis, 5(1), 12–28. https://doi.org/10.53006/rna.974148
   Google Scholar
• Sahu, P. K., & Saha Ray, S. (2018). Comparison on wavelets techniques for solving fractional optimal control problems. Journal of Vibration and Control, 24(6), 1185–1201. https://doi.org/10.1177/1077546316659611
   Web of Science ®Google Scholar
• Shahini, M., & Mehrpouya, M. A. (2021). Transformed orthogonal functions for solving infinite horizon fractional optimal control problems. European Journal of Control, 59, 13–28. https://doi.org/10.1016/j.ejcon.2021.01.005
   Web of Science ®Google Scholar
• Sweilam, N. H., Nagy, A. M., & T. M. Al-Ajami (2021). Numerical solutions of fractional optimal control with Caputo-Katugampola derivative. Advances in Difference Equations, 2021(1), 1–16. https://doi.org/10.1186/s13662-021-03580-w
   Web of Science ®Google Scholar
• Xiaobing, P., Yang, X., Noori Skandari, M. H., Tohidi, E., & Shateyi, S. (2022). A new high accurate approximate approach to solve optimal control problems of fractional order via efficient basis functions. Alexandria Engineering Journal, 61(8), 5805–5818. https://doi.org/10.1016/j.aej.2021.11.007
   Web of Science ®Google Scholar