An outlook on the controllability of non-instantaneous impulsive neutral fractional nonlocal systems via Atangana–Baleanu–Caputo derivative

References

• Abbas, M. I. (2021). Nonlinear Atangana–Baleanu fractional differential equations involving the Mittag-Leffler integral operator. Memoirs on Differential Equations and Mathematical Physics, 83, 1–11.
   Web of Science ®Google Scholar
• Abdeljawad, T., & Baleanu, D. (2016). Discrete fractional differences with nonsingular discrete Mittag-Leffler kernels. Advances in Difference Equations, 2016(1), 1–18. doi:10.1186/s13662-016-0949-5
   Google Scholar
• Abdeljawad, T., & Baleanu, D. (2017). Integration by parts and its applications of a new nonlocal fractional derivative with Mittag-Leffler nonsingular kernel. Journal of Nonlinear Sciences and Applications, 10(3), 1098–1107. doi:10.22436/jnsa.010.03.20
   Google Scholar
• Agrawal, O. P. (2004). A general formulation and solution scheme for fractional optimal control problems. Nonlinear Dynamics, 38(1–4), 323–337. doi:10.1007/s11071-004-3764-6
   Web of Science ®Google Scholar
• Agrawal, O. P. (2008). Fractional optimal control of a distributed system using eigenfunctions. Journal of Computational and Nonlinear Dynamics, 3(2), 1–6. doi:10.1115/1.2833873
   Web of Science ®Google Scholar
• Aimene, D., Baleanu, D., & Seba, D. (2019). Controllability of semilinear impulsive Atangana–Baleanu fractional differential equations with delay. Chaos Solitons Fractals, 128, 51–57. doi:10.1016/j.chaos.2019.07.027
   Web of Science ®Google Scholar
• Anurag Shukla, N. S., & Pandey, D. N. (2015). Approximate controllability of semilinear fractional control systems of order α ∈ (1,2]. 2015 proceedings of the conference on control and its applications, 175–180.
   Google Scholar
• Atangana, A., & Baleanu, D. (2016). New fractional derivatives with non-local and non-singular kernel: Theory and application to heat transfer model. Thermal Science, 20(2), 763–769. doi:10.2298/TSCI160111018A
   Web of Science ®Google Scholar
• Bahaa, G. M., & Hamiaz, A. (2018). Optimality conditions for fractional differential inclusions with nonsingular Mittag-Leffler kernel. Advances in Differential Equations, 2018, 1–26. doi:10.1186/s13662-018-1706-8
   Google Scholar
• Balasubramaniam, P. (2021). Controllability of semilinear noninstantaneous impulsive ABC neutral fractional differential equations. Chaos Solitons Fractals, 152, 111276. doi:10.1016/j.chaos.2021.111276
   Web of Science ®Google Scholar
• Balder, E. (1987). Necessary and sufficient conditions for L1-strong-weak lower semicontinuity of integral functional. Nonlinear Analysis: Real World Applications, 11(12), 1399–1404. doi:10.1016/0362-546X(87)90092-7
   Google Scholar
• Baleanu, D., & Fernandez, A. (2018). On some new properties of fractional derivatives with Mittag-Leffler kernel. Communications in Nonlinear Science and Numerical Simulation, 59, 444–462. doi:10.1016/j.cnsns.2017.12.003
   Web of Science ®Google Scholar
• Banas, J. (1980). On measures of noncompactness in Banach spaces. Commentationes Mathematicae Universitatis Carolinae, 21(1), 131–143. doi: http://eudml.org/doc/17021
   Google Scholar
• Bedi, P., Kumar, A., & Khan, A. (2021). Controllability of neutral impulsive fractional differential equations with Atangana–Baleanu–Caputo derivatives. Chaos, Solitons & Fractals, 150, 111153. doi:10.1016/j.chaos.2021.111153
   Web of Science ®Google Scholar
• Benchohra, M., & Seba, D. (2009). Impulsive fractional differential equations in Banach spaces. Electronic Journal of Qualitative Theory of Differential Equations, 8(8), 1–14. doi:10.14232/ejqtde.2009.4.8
   Google Scholar
• Caputo, M., & Fabrizio, M. (2015). A new definition of fractional derivative without singular kernel. Progress in Fractional Differentiation and Applications, 1, 73–85. doi:10.12785/pfda/010201
   Google Scholar
• Chalishajar, D., Ravichandran, C., Dhanalakshmi, S., & Murugesu, R. (2019). Existence of fractional impulsive functional integro-differential equations in Banach spaces. Applied System Innovation, 2(2), 18. doi:10.3390/asi2020018
   Google Scholar
• Devi, A., & Kumar, A. (2021). Existence and uniqueness results for integro fractional differential equations with Atangana–Baleanu fractional derivative. Journal of Mathematical Extension, 15(5), 1–24. doi:10.30495/JME.SI.2021.2128
   Google Scholar
• Dineshkumar, C., & Hoon Joo, Y. (2023). A note concerning to approximate controllability of Atangana–Baleanu fractional neutral stochastic integro-differential system with infinite delay. Mathematical Methods in the Applied Sciences, 46(9), 9922–9941. doi:10.1002/mma.9093
   Web of Science ®Google Scholar
• Dineshkumar, C., Udhayakumar, R., Vijayakumar, V., Nisar, K. S., & Shukla, A. (2022). A note concerning to approximate controllability of Atangana–Baleanu fractional neutral stochastic systems with infinite delay. Chaos, Solitons & Fractals, 157, 111916. doi:10.1016/j.chaos.2022.111916
   Web of Science ®Google Scholar
• Dineshkumar, C., Udhayakumar, R., Vijayakumar, V., Shukla, A., & Sooppy Nisar, K. (2023). Discussion on the approximate controllability of nonlocal fractional derivative by Mittag-Leffler kernel to stochastic differential systems. Qualitative Theory of Dynamical Systems, 22(1), 27. doi:10.1007/s12346-022-00725-4
   Web of Science ®Google Scholar
• Dineshkumar, C., Udhayakumar, R., Vijayakumar, V., Sooppy Nisar, K., Shukla, A., Abdel-Aty, A.-H., … Mahmoud, E. E. (2022). A note on existence and approximate controllability outcomes of Atangana–Baleanu neutral fractional stochastic hemivariational inequality. Results in Physics, 38, 105647. doi:10.1016/j.rinp.2022.105647
   Web of Science ®Google Scholar
• Enes, A., Onur Kıymaz I. (2023). New generalized Mellin transform and applications to partial and fractional differential equations. International Journal of Mathematics and Computer in Engineering, 1(1), 1–21. https://doi.org/10.2478/ijmce-2023-0004
   Google Scholar
• Gautam, G. R., & Dabas, J. (2015). Mild solutions for class of neutral fractional functional differential equations with not instantaneous impulses. Applied Mathematics and Computation, 259, 480–489. doi:10.1016/j.amc.2015.02.069
   Web of Science ®Google Scholar
• Goufo, E. F. D., Ravichandran, C., & Birajdar, G. A. (2021). Self-similarity techniques for chaotic attractors with many scrolls using step series switching. Mathematical Modelling and Analysis, 26(4), 591–611. doi:10.3846/mma.2021.13678
   Web of Science ®Google Scholar
• Gupta, V., Jarad, F., Valliammal, N., Ravichandran, C., & Nisar, K. S. (2022). Existence and uniqueness of solutions for fractional nonlinear hybrid impulsive system. Numerical Methods for Partial Differential Equations, 38(3), 359–371. doi:10.1002/num.22628
   Web of Science ®Google Scholar
• Jarad, F., Abdeljawad, T., & Hammouch, Z. (2018). On a class of ordinary differential equations in the frame of Atangana–Baleanu derivative. Chaos Solitons Fractals, 117, 16–20. doi:10.1016/j.chaos.2018.10.006
   Web of Science ®Google Scholar
• Jothimani, K., Kaliraj, K., Panda, S. K., Nisar, K. S., & Ravichandran, C. (2021). Results on controllability of non-densely characterized neutral fractional delay differential system. Evolution Equations & Control Theory, 10(3), 619–631. doi:10.3934/eect.2020083
   Google Scholar
• Kaliraj, K., Thilakraj, E., Ravichandran, C., & Nisar, K. S. (2021). Controllability analysis for impulsive integro-differential equation via Atangana–Baleanu fractional derivative. Mathematical Methods in the Applied Sciences, 2021, 1–10. doi:10.1002/mma.7693
   Google Scholar
• Kavitha Williams, W., Vijayakumar, V., Nisar, K. S., & Shukla, A. (2023). Atangana–Baleanu semilinear fractional differential inclusions with infinite delay: Existence and approximate controllability. Journal of Computational and Nonlinear Dynamics, 18(2), 1–25. doi:10.1115/1.4056357
   Web of Science ®Google Scholar
• Kavitha Williams, W., Vijayakumar, V., Shukla, A., & Nisar, K. S. (2022). An analysis on approximate controllability of Atangana–Baleanu fractional semilinear control systems. International Journal of Nonlinear Sciences and Numerical Simulation, 2022, 1–12. doi:10.1515/ijnsns-2021-0371
   Google Scholar
• Kilbas, A. A., Srivastava, H. M., & Trujillo, J. J. (2006). Theory and applications of fractional differential equations. New York, Amsterdam: Elsevier Science Inc.
   Google Scholar
• Kumar, A., & Pandey, D. N. (2020). Existence of mild solution of Atangana–Baleanu fractional differential equations with non-instantaneous impulses and with non-local conditions. Chaos Solitons Fractals, 132, 109551. doi:10.1016/j.chaos.2019.109551
   Web of Science ®Google Scholar
• Kumar, V., Kostic, M., & Pinto, M. (2023). Controllability results for fractional neutral differential systems with non-instantaneous impulses. Journal of Fractional Calculus and Applications, 14, 1–20. doi: http://mathfrac.org/Journals/JFCA/
   Google Scholar
• Liu, S., & Wang, J. (2017). Optimal controls of systems governed by semilinear fractional differential equations with not instantaneous impulses. Journal of Optimization Theory and Applications. 174, 455–473. doi:10.1007/s10957-017-1122-3
   Web of Science ®Google Scholar
• Ma, Y.-K., Dineshkumar, C., Vijayakumar, V., Udhayakumar, R., Shukla, A., & Nisar, K. S. (2023). Approximate controllability of Atangana–Baleanu fractional neutral delay integrodifferential stochastic systems with nonlocal conditions. Ain Shams Engineering Journal, 14(3), 101882. doi:10.1016/j.asej.2022.101882
   Web of Science ®Google Scholar
• Mahmud, A. A., Tanriverdi, T., & Muhamad, K. A. (2023). Exact traveling wave solutions for (2 + 1)-dimensional Konopelchenko–Dubrovsky equation by using the hyperbolic trigonometric functions methods. International Journal of Mathematics and Computer in Engineering, 1(1), 1–14. doi:10.2478/ijmce-2023-0002
   Google Scholar
• Miller, K., & Ross, B. (1993). An introduction to the fractional calculus and differential equations. New York: John Wiley.
   Google Scholar
• Nisar, K. S., Jothimani, K., Kaliraj, K., & Ravichandran, C. (2021). An analysis of controllability results for nonlinear Hilfer neutral fractional derivatives with non-dense domain. Chaos Solitons Fractals, 146, 110915. doi:10.1016/j.chaos.2021.110915
   Web of Science ®Google Scholar
• Pandey, D. N., Das, S., & Sukavanam, N. (2014). Existence of solutions for a second order neutral differential equation with state dependent delay and not instantaneous impulses. International Journal of Nonlinear Sciences, 18, 145–155. IJNS.2014.10.15/833
   Google Scholar
• Pazy, A. (1983). Semigroups of linear operators and applications to partial differential equations. New York: Springer-Verlag.
   Google Scholar
• Podlubny, I. (1999). Fractional differential equations: An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications. San Diego: Academic Press.
   Google Scholar
• Ravichandran, C., Jothimani, K., Nisar, K. S., Mahmoud, E. E., & Yahia, I. S. (2022). An interpretation on controllability of Hilfer fractional derivative with nondense domain. Alexandria Engineering Journal, 61(12), 9941–9948. doi:10.1016/j.aej.2022.03.011
   Web of Science ®Google Scholar
• Ruhil, S., & Malik, M. (2023). Inverse problem for the Atangana–Baleanu fractional differential equation. Journal of Inverse and Ill-Posed Problems. doi:10.1515/jiip-2022-0025
   Google Scholar
• Shukla, A., Nagarajan, S., & Pandey, D. N. (2016). Complete controllability of semilinear stochastic systems with delay in both state and control. Mathematical Reports, 18(2), 257–259. doi: http://repository.iitr.ac.in/handle/123456789/9793
   Web of Science ®Google Scholar
• Shukla, A., Sukavanam, N., & Pandey, D. N. (2014). Controllability of semilinear stochastic system with multiple delays in control. IFAC Proceedings Volumes, 47(1), 306–312. doi:10.3182/20140313-3-IN-3024.00107
   Google Scholar
• Tajadodi, H., Khan, A., Francisco Gómez-Aguilar, J., & Khan, H. (2021). Optimal control problems with Atangana–Baleanu fractional derivative. Optimal Control Applications and Methods, 42(1), 96–109. doi:10.1002/oca.2664
   Web of Science ®Google Scholar
• Vijayakumar, V., Nisar, K. S., Chalishajar, D., Shukla, A., Malik, M., Alsaadi, A., & Aldosary, S. F. (2022). A note on approximate controllability of fractional semilinear integrodifferential control systems via resolvent operators. Fractal and Fractional, 6(2), 73. doi:10.3390/fractalfract6020073
   Web of Science ®Google Scholar
• Yang, H., Agarwal, R. P., & Liang, Y. (2016). Controllability for a class of integro-differential evolution equations involving nonlocal initial conditions. International Journal of Control, 90(12), 1–13. doi:10.1080/00207179.2016.1260161
   Web of Science ®Google Scholar
• Yang, X. J. (2019). General fractional derivatives: Theory, methods and applications (1st ed.). Taylor & Francis Group, Boca Raton: CRC Press.
   Google Scholar