[
[1] S. Adler, Quaternionic Quantum Mechanics and Quantum Fields. Oxford University Press, New York, 1994.
]Search in Google Scholar
[
[1] R.P. Agarwal, C. Wang, D. O’Regan, Recent development of time scales and related topics on dynamic equations. Mem. Differential Equations Math. Phys. 67 (2016) 131-135.
]Search in Google Scholar
[
[3] F.M. Atici, G.Sh. Guseinov, On Green’s functions and positive solutions for boundary value problems on time scales, J. Comput. Appl. Math. 18, (2002) 75-99.
]Search in Google Scholar
[
[4] M. Bohner, A. Peterson, Dynamic Equations on Time Scales, An Introduction with Applications. Birkhauser, Boston, 2001.10.1007/978-1-4612-0201-1
]Search in Google Scholar
[
[5] Z. Cai, K.I. Kou, Laplace transform: a new approach in solving linear quaternion differential equations, Math. Meth. Appl. Sci. 41, (2018) 4033-4048.
]Search in Google Scholar
[
[6] D. Cheng, K.I. Kou, Y.H. Xia, A unified analysis of linear quaternion dynamic equations on time scales, J. Appl. Anal. Comput. 8, (2018) 172-201.
]Search in Google Scholar
[
[7] D.J. Gibbon, D.D. Holm, R.M. Kerr, I. Roulstone, Quaternions and particle dynamics in the Euler fluid equations, Nonlinearity, 19, (2006) 1969-1983.10.1088/0951-7715/19/8/011
]Search in Google Scholar
[
[8] W.R. Hamilton, Elements of Quaternions. London, UK: Longmans, Green, & Co, 1866.
]Search in Google Scholar
[
[9] S. Hilger, Ein Maßkettenkalkül mit Anwendung auf Zentrumsmannig-faltigkeiten, Ph.D. Thesis, Universit¨at Würzburg, 1988.
]Search in Google Scholar
[
[10] K.I. Kou, Y.H. Xia, Linear quaternion differential equations: basic theory and fundamental results, Stud. Appl. Math. 141, (2018) 3-45.
]Search in Google Scholar
[
[11] V. Lakshmikantham, D.D. Bainov, P.S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, Singapore, 1989.10.1142/0906
]Search in Google Scholar
[
[12] Z. Li, C. Wang, R.P. Agarwal, The non-eigenvalue form of Liouville’s formula and α-matrix exponential solutions for combined matrix dynamic equations on time scales, Mathematics, 7(10), 962; https://doi.org/10.3390/math7100962 (2019).10.3390/math7100962
]Search in Google Scholar
[
[13] Z. Li, C. Wang, R.P. Agarwal, D. O’Regan, Commutativity of quaternion-matrix-valued functions and quaternion matrix dynamic equations on time scales, Stud. Appl. Math., 146, (2021) 139-210.10.1111/sapm.12344
]Search in Google Scholar
[
[14] Z. Li, C. Wang, R.P. Agarwal, R. Sakthivel, Hyers-Ulam-Rassias stability of quaternion multidimensional fuzzy nonlinear difference equations with impulses, Iranian J. Fuzzy Syst., 10.22111/IJFS.2021.5950 (2021).
]Search in Google Scholar
[
[15] Z. Li, C. Wang, Cauchy matrix and Liouville formula of quaternion impulsive dynamic equations on time scales, Open Math., 18, (2020) 353-377.10.1515/math-2020-0021
]Search in Google Scholar
[
[16] G. Qin, C. Wang, Lebesgue-Stieltjes combined ♢α-measure and integral on time scales, Rev. R. Acad. Cienc. Exactas F´ıs. Nat. Ser. A Mat. RAC-SAM. https://doi.org/10.1007/s13398-021-01000-y, 115:50 (2021).10.1007/s13398-021-01000-y
]Search in Google Scholar
[
[17] J.W. Rogers, Q. Sheng, Notes on the diamond-α dynamic derivative on time scales, J. Math. Anal. Appl. 326, (2007) 228-241.
]Search in Google Scholar
[
[18] Q. Sheng, M. Fadag, J. Henderson, J.M. Davis, An exploration of combined dynamic derivatives on time scales and their applications, Nonlinear Anal.: RWA. 7, (2006) 395-413.
]Search in Google Scholar
[
[19] C. Wang, R.P. Agarwal, Almost periodic dynamics for impulsive delay neural networks of a general type on almost periodic time scales, Commun. Nonlinear Sci. Numer. Simulat. 36, (2016) 238-251.
]Search in Google Scholar
[
[20] C. Wang, R.P. Agarwal, D. O’Regan, R. Sakthivel, A computation method of Hausdorff distance for translation time scales, 99, (2020) 1218-1247.10.1080/00036811.2018.1529303
]Search in Google Scholar
[
[21] C. Wang, R.P. Agarwal, Relatively dense sets, corrected uniformly almost periodic functions on time scales, and generalizations, Adv. Differ. Equa. 2015:312, (2015) 1-9.
]Search in Google Scholar
[
[22] C. Wang, R.P. Agarwal, D. O’Regan, Periodicity, almost periodicity for time scales and related functions. Nonauton. Dyn. Syst. 3, (2016) 24-41.
]Search in Google Scholar
[
[23] C. Wang, R.P. Agarwal, D. O’Regan, δ-almost periodic functions and applications to dynamic equations, Mathematics 7, 525, doi.org/10.3390/math7060525 (2019).10.3390/math7060525
]Search in Google Scholar
[
[24] C. Wang, R. Sakthivel, G.M. N’Guérékata, S-almost automorphic solutions for impulsive evolution equations on time scales in shift operators, Mathematics, 8(6), 1028; https://doi.org/10.3390/math8061028 (2020).10.3390/math8061028
]Search in Google Scholar
[
[25] C. Wang, R.P. Agarwal and D. O’Regan, Calculus of fuzzy vector-valued functions and almost periodic fuzzy vector-valued functions on time scales, Fuzzy. Sets and Syst., 375 (2019) 1-52.
]Search in Google Scholar
[
[26] C. Wang, Almost periodic solutions of impulsive BAM neural networks with variable delays on time scales. Commun. Nonlinear Sci. Numer. Simul. 19, (2014) 2828-2842.
]Search in Google Scholar
[
[27] C. Wang, R.P. Agarwal, A Further study of almost periodic time scales with some notes and applications Abstr. Appl. Anal., Article ID 267384, (2014) 1-12.10.1155/2014/267384
]Search in Google Scholar
[
[28] C. Wang, R.P. Agarwal, Weighted piecewise pseudo almost automorphic functions with applications to abstract impulsive ∇-dynamic equations on time scales, Adv. Differ. Equa. 2014:153, (2014) 1-29.
]Search in Google Scholar
[
[29] C. Wang, R.P. Agarwal, D. O’Regan, Π-semigroup for invariant under translations time scales and abstract weighted pseudo almost periodic functions with applications. Dyn. Syst. Appl. 25, (2016) 1-28.
]Search in Google Scholar
[
[30] C. Wang, R.P. Agarwal, A classification of time scales and analysis of the general delays on time scales with applications. Math. Meth. Appl. Sci. 39, (2016) 1568-1590.
]Search in Google Scholar
[
[31] C. Wang, R.P. Agarwal, Almost automorphic functions on semigroups induced by complete-closed time scales and application to dynamic equations, Discret. Continu. Dynam. Syst. B. 25, (2020) 781-798.
]Search in Google Scholar
[
[32] C. Wang, R.P. Agarwal, D. O’Regan, R. Sakthivel, Local pseudo almost automorphic functions with applications to semilinear dynamic equations on changing-periodic time scales, Bound Value Probl. 133, doi:10.1186/s13661-019-1247-4 (2019).10.1186/s13661-019-1247-4
]Search in Google Scholar
[
[33] C. Wang, R.P. Agarwal, D. O’Regan, Local-periodic solutions for functional dynamic equations with infinite delay on changing-periodic time scales, Math. Slovaca. 68, (2018) 1397-1420.
]Search in Google Scholar
[
[34] C. Wang, R.P. Agarwal, Changing-periodic time scales and decomposition theorems of time scales with applications to functions with local almost periodicity and automorphy, Adv. Differ. Equa. 2015:296 (2015) 1-21.
]Search in Google Scholar
[
[35] C. Wang, R.P. Agarwal, D. O’Regan, A matched space for time scales and applications to the study on functions, Adv. Differ. Equa. 2017:305, (2017) 1-28.
]Search in Google Scholar
[
[36] C. Wang, R.P. Agarwal, D. O’Regan, n0-order ∆-almost periodic functions and dynamic equations, Applic. Anal. 97, (2018) 2626-2654.
]Search in Google Scholar
[
[37] C. Wang, R.P. Agarwal, D. O’Regan, Weighted pseudo δ-almost automorphic functions and abstract dynamic equations, Georgian Math. J. doi: https://doi.org/10.1515/gmj-2019-2066 (2019) (In press).10.1515/gmj-2019-2066
]Search in Google Scholar
[
[38] C. Wang, R.P. Agarwal, R. Sakthivel, Almost periodic oscillations for delay impulsive stochastic Nicholson’s blowflies timescale model, Comput. Appl. Math. 37, (2018) 3005-3026.
]Search in Google Scholar
[
[39] C. Wang, R.P. Agarwal, Almost periodic solution for a new type of neutral impulsive stochastic Lasota-Wazewska timescale model, Appl. Math. Lett. 70, (2017) 58-65.
]Search in Google Scholar
[
[40] C. Wang, R. Sakthivel, Double almost periodicity for high-order Hopfield neural networks with slight vibration in time variables, Neurocomputing, 282, (2018) 1-15.10.1016/j.neucom.2017.12.008
]Search in Google Scholar
[
[41] C. Wang, R.P. Agarwal, D. O’Regan, R. Sakthivel, Theory of Translation Closedness for Time Scales, Developments in Mathematics, Vol. 62, Springer, Switzerland, 2020.10.1007/978-3-030-38644-3
]Search in Google Scholar
[
[42] C. Wang, G. Qin, R.P. Agarwal, D. O’Regan, ♢α-Measurability and combined measure theory on time scales, Applic. Anal., https://doi.org/10.1080/00036811.2020.1820997, 2020 (In press).10.1080/00036811.2020.1820997
]Search in Google Scholar
[
[43] C. Wang, R.P. Agarwal, D. O’Regan, Matrix measure on time scales and almost periodic analysis of the impulsive Lasota-Wazewska model with patch structure and forced perturbations, Math. Meth. Appl. Sci. 39, (2016) 5651-5669.
]Search in Google Scholar
[
[44] C. Wang, Piecewise pseudo almost periodic solution for impulsive non-autonomous highorder Hopfield neural networks with variable delays, Neurocomputing, 171, (2016) 1291-1301.10.1016/j.neucom.2015.07.054
]Search in Google Scholar
[
[45] C. Wang, R.P. Agarwal, Uniformly rd-piecewise almost periodic functions with applications to the analysis of impulsive ∆-dynamic system on time scales, Appl. Math. Comput. 259, (2015) 271-292.
]Search in Google Scholar
[
[46] C. Wang, R.P. Agarwal, D. O’Regan, Weighted piecewise pseudo double-almost periodic solution for impulsive evolution equations. J. Nonlinear Sci. Appl. 10, (2017) 3863-3886.10.22436/jnsa.010.07.41
]Search in Google Scholar
[
[47] C. Wang, R.P. Agarwal, D. O’Regan, Compactness criteria and new impulsive functional dynamic equations on time scales, Adv. Differ. Equa. 2016:197, (2016) 1-41.
]Search in Google Scholar
[
[48] C. Wang, R.P. Agarwal, Exponential dichotomies of impulsive dynamic systems with applications on time scales, Math. Meth. Appl. Sci. 38, (2015) 3879-3900.
]Search in Google Scholar
[
[49] C. Wang, R.P. Agarwal, D. O’Regan, R. Sakthivel, Discontinuous generalized double-almost-periodic functions on almost-complete-closed time scales, Bound Value Probl. 165, doi.org/10.1186/s13661-019-1283-0 (2019).10.1186/s13661-019-1283-0
]Search in Google Scholar
[
[50] C. Wang, Z. Li, R. P. Agarwal, D. O’Regan, Coupled-jumping timescale theory and applications to time-hybrid dynamic equations, convolution and Laplace transforms. Dynam. Syst. Appl., 30 (2021) 461-508.
]Search in Google Scholar
[
[51] P. Wilczynski, Quaternionic-valued ordinary differential equations. The Riccati equation, J. Differ. Equ. 247, (2009) 2163-2187.
]Search in Google Scholar
[
[52] F. Zhang, Quaternions and matrices of quaternions, Linear Algebra and its Applications, 251, (1997) 21-57.10.1016/0024-3795(95)00543-9
]Search in Google Scholar
[
[53] J. Zhu, J. Sun, Existence and uniqueness results for quaternion-valued nonlinear impulsive differential systems, J. Syst. Sci. Compl. 31, (2018) 596-607.
]Search in Google Scholar
[
[54] J. Zhu, J. Sun, Global exponential stability of Clifford-valued recurrent neural networks, Neurocomputing, 173, (2016) 685-689.10.1016/j.neucom.2015.08.016
]Search in Google Scholar
