A computation method of Hausdorff distance for translation time scales

References

• Hilger S. Ein Maβkettenkalkül mit Anwendung auf Zentrumsmannigfaltigkeiten [Ph.D. thesis]. Universität Würzburg; 1988.
   Google Scholar
• Bohner M, Peterson A. Dynamic equations on time scales. Boston, MA: Birkhäuser Boston Inc.; 2001.
   Google Scholar
• Bohner M, Peterson A. Advances in dynamic equations on time scales. Boston, MA: Birkhäuser Boston Inc.; 2003.
   Google Scholar
• Atici FM, Biles DC, Lebedinsky A. An application of time scales to economics. Math Comput Modell. 2006;43:718–726. doi: 10.1016/j.mcm.2005.08.014
   Web of Science ®Google Scholar
• Atici FM, Eloe PW. Fractional q-calculus on a time scale. J Nonlinear Math Phys. 2007;14:341–352. doi: 10.2991/jnmp.2007.14.3.4
   Web of Science ®Google Scholar
• Ogulenko A. Asymptotical properties of social network dynamics on time scales. J Comput Appl Math. 2017;319:413–422. doi: 10.1016/j.cam.2017.01.031
   Web of Science ®Google Scholar
• Benkhettou N, Hassani S, Torres DFM. A conformable fractional calculus on arbitrary time scales. J King Saud Univ-Sci. 2016;28:93–98. doi: 10.1016/j.jksus.2015.05.003
   Web of Science ®Google Scholar
• Jafari H, Haghbin A, Johnston SJ, Baleanu D. A new algorithm for solving dynamic equations on a time scale. J Comput Appl Math. 2017;312:167–173. doi: 10.1016/j.cam.2016.02.047
   Web of Science ®Google Scholar
• Benkhettou N, Hammoudi A, Torres DFM. Existence and uniqueness of solution for a fractional Riemann–Liouville initial value problem on time scales. J King Saud Univ-Sci. 2016;28:87–92. doi: 10.1016/j.jksus.2015.08.001
   Web of Science ®Google Scholar
• Atici FM, McMahan CS. A comparison in the theory of calculus of variations on time scales with an application to the Ramsey model. Nonlinear Dyn Syst Theory. 2009;9:1–10.
   Google Scholar
• Baleanu D, Bhrawy AH, Torres DFM, Salahshour S. Fractional and time-scales differential equations. Abstr Appl Anal. 2014;2014:1–2. (Article ID 365250).
   Google Scholar
• Ji D, Yang L, Zhang J. Almost periodic functions on Hausdorff almost periodic time scales. Adv Differ Equ. 2017;103:1–14.
   Google Scholar
• Wang C, Agarwal RP. A further study of almost periodic time scales with some notes and applications. Abstr Appl Anal. 2014;2014:1–11. (Article ID 267384).
   Google Scholar
• Wang C, Agarwal RP, O'Regan D. Weighted piecewise pseudo double-almost periodic solution for impulsive evolution equations. J Nonlinear Sci Appl. 2017;10:3863–3886. doi: 10.22436/jnsa.010.07.41
   Google Scholar
• Agarwal RP, O'Regan D. Some comments and notes on almost periodic functions and changing-periodic time scales. Electr J Math Anal Appl. 2018;6:125–136.
   Google Scholar
• Wang C, Agarwal RP, O'Regan D. A matched space for time scales and applications to the study on functions. Adv Differ Equ. 2017;305:1–28.
   Google Scholar
• Wang C, Agarwal RP, O'Regan D. n0-order Δ-almost periodic functions and dynamic equations. Appl Anal. 2017;1–29. doi:10.1080/00036811.2017.1382689
   Web of Science ®Google Scholar
• Wang C, Agarwal RP, O'Regan D. Periodicity almost periodicity for time scales and related functions. Nonauton Dyn Syst. 2016;3:24–41.
   Google Scholar
• Wang C, Agarwal RP. A classification of time scales and analysis of the general delays on time scales with applications. Math Meth Appl Sci. 2016;239:1568–1590. doi: 10.1002/mma.3590
   Web of Science ®Google Scholar
• Jahn KU. Evaluation of Hausdorff distances in interval mathematics. Computing. 1990;45:69–77. doi: 10.1007/BF02250585
   Web of Science ®Google Scholar
• Diagana T. Weighted pseudo almost periodic functions and applications. Comp Rend Math. 2006;343:643–646. doi: 10.1016/j.crma.2006.10.008
   Web of Science ®Google Scholar
• Diagana T, Mophou GM, N'Guérékata GM. Existence of weighted pseudo-almost periodic solutions to some classes of differential equations with Sp-weighted pseudo-almost periodic coefficients. Nonlinear Anal TMA. 2010;72:430–438. doi: 10.1016/j.na.2009.06.077
   Web of Science ®Google Scholar
• Diagana T, N'Guérékata GM. Stepanov-like almost automorphic functions and applications to some semilinear equations. Appl Anal. 2007;86:723–733. doi: 10.1080/00036810701355018
   Web of Science ®Google Scholar
• N'Guérékata GM. Existence and uniqueness of almost automorphic mild solutions to some semilinear abstract differential equations. Semigroup Forum. 2004;69:80–86. doi: 10.1007/s00233-003-0021-0
   Web of Science ®Google Scholar
• N'Guérékata GM. Almost automorphic and almost periodic functions in abstract spaces. New York: Kluwer Academic; 2001.
   Google Scholar
• N'Guérékata GM. Topics in almost automorphy. New York: Springer; 2005.
   Google Scholar
• Alzabut JO, Nieto JJ, Stamov GT. Existence and exponential stability of positive almost periodic solutions for a model of hematopoiesis. Bound Value Probl. 2009;2009:1–10. (Article ID 127510). doi: 10.1155/2009/127510
   Web of Science ®Google Scholar
• Stamov GT. On the existence of almost periodic solutions for the impulsive Lasota–Wazewska model. Appl Math Lett. 2009;22:516–520. doi: 10.1016/j.aml.2008.07.002
   Web of Science ®Google Scholar
• Stamov GT, Alzabut JO. Almost periodic solutions for abstract impulsive differential equations. Nonlinear Anal TMA. 2010;72:2457–2464. doi: 10.1016/j.na.2009.10.042
   Web of Science ®Google Scholar
• Stamov IM, Stamov GT, Alzabut JO. Global exponential stability for a class of impulsive BAM neural networks with distributed delays. Appl Math Inf Sci. 2013;7:1539–1546. doi: 10.12785/amis/070438
   Google Scholar
• Conway JB. A course in functional analysis. New York: Springer-Verlag; 1985.
   Google Scholar
• Oxtoby JC. Measure and category. New York: Springer-Verlag; 1980.
   Google Scholar