n₀-order Δ-almost periodic functions and dynamic equations

References

• Bohr H . Zur Theorie der fastperiodischen Funktionen I. Acta Math. 1925;45:129–127.
   Google Scholar
• Besicovitch AS . On generalized almost periodic functions. Proc London Math Soc. 1926;25:495–512.
   Google Scholar
• Stepanov V . Ueber einige Verallgemeinerungen der fastperiodischen Funktionen. Math Ann. 1925;45:473–498.
   Google Scholar
• Weyl H . Integralgleichungen und fastperiodische Funktionen. Math Ann. 1927;97:338–356.
   Google Scholar
• Diagana T , Mophou GM , N’Guérékata GM . Existence of weighted pseudo-almost periodic solutions to some classes of differential equations with S p -weighted pseudo-almost periodic coefficients. Nonlinear Anal TMA. 2010;72:430–438.
   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.
   Web of Science ®Google Scholar
• Xiao T , Liang J , Zhang J . Pseudo almost automorphic solutions to semilinear differential equations in Banach spaces. Semigroup Forum. 2008;76:518–524.
   Web of Science ®Google Scholar
• N’Guérékata GM . Topics in Almost Automorphy. New York (NY): Springer; 2005.
   Google Scholar
• Liang Jin , Zhang Jun , Xiao Ti-Jun . Composition of pseudo almost automorphic and asymptotically almost automorphic functions. J Math Anal Appl. 2008;340:1493–1499.
   Web of Science ®Google Scholar
• Liang J , N’Guérékata GM , Xiao T , et al . Some properties of pseudo-almost automorphic functions and applications to abstract differential equations. Nonlinear Anal TMA. 2009;70:2731–2735.
   Web of Science ®Google Scholar
• Ezzinbi K , N’Guérékata GM . Massera type theorem for almost automorphic solutions of functional differential equations of neutral type. J Math Anal Appl. 2006;316:707–721.
   Web of Science ®Google Scholar
• Hilger S . Ein Maβkettenkalkül mit Anwendung auf Zentrumsmannigfaltigkeiten [Ph.D. thesis]. Universität. Würzburg. 1988. German
   Google Scholar
• Akhmet MU , Turan M . Differential equations on variable time scales. Nonlinear Anal Theory Meth Appl. 2009;70:1175–1192.
   Web of Science ®Google Scholar
• Akhmet MU , Turan M . The differential equations on time scales through impulsive differential equations. Nonlinear Anal Theor Meth Appl. 2006;65:2043–2060.
   Web of Science ®Google Scholar
• Wang C . Almost periodic solutions of impulsive BAM neural networks with variable delays on time scales. Commun Nonlinear Sci Numer Simul. 2014;19:2828–2842.
   Web of Science ®Google Scholar
• Wang C , Agarwal RP , O’Regan D . Matrix measure on time scales and almost periodic analysis of the impulsive Lasota-Wazewska model with patch structure and forced perturbations. Math Meth App Sci. 2016;39:5651–5669.
   Web of Science ®Google Scholar
• Wang C , Agarwal RP . Changing-periodic time scales and decomposition theorems of time scales with applications to functions with local almost periodicity and automorphy. Adv Differ Equ. 2015;296:1–21.
   Google Scholar
• Wang C , Agarwal RP . Relatively dense sets, corrected uniformly almost periodic functions on time scales, and generalizations. Adv Differ Equ. 2015;312:1–9.
   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 , O’Regan D . π-semigroup for invariant under translations time scales and abstract weighted pseudo almost periodic functions with applications. Dyn Syst Appl. 2016;25:1–28.
   Web of Science ®Google Scholar
• Wang C , Agarwal RP . Almost periodic dynamics for impulsive delay neural networks of a general type on almost periodic time scales. Commun Nonlinear Sci Numer Simul. 2016;36:238–251.
   Web of Science ®Google Scholar
• Wang C , Agarwal RP . Uniformly rd-piecewise almost periodic functions with applications to the analysis of impulsive Δ-dynamic system on time scales. Appl Math Comput. 2015;259:271–292.
   Web of Science ®Google Scholar
• Bohner M , Chieochan R . The Beverton--Holt q-difference equation. J Biol Dyn. 2013;7:86–95.
   PubMed Web of Science ®Google Scholar
• Ahmad B , Ntouyas SK , Tariboon J , et al . Impulsive fractional q-integro-difference equations with separated boundary conditions. Appl Math Comput. 2016;281:199–213.
   Web of Science ®Google Scholar
• Adıvar M . A new periodic concept for time scales. Math Slovaca. 2013;63:817–828.
   Web of Science ®Google Scholar
• Adıvar M , Raffoul YN . Existence of resolvent for Volterra integral equations on time scales. Bull Aust Math Soc. 2010;82:139–155.
   Web of Science ®Google Scholar
• Wang C , Agarwal RP . A classification of time scales and analysis of the general delays on time scales with applications. J Math. 2016;39:1568–1590.
   Google Scholar
• Bohner M , Peterson A . Dynamic equations on time scales. An introduction with applications. Boston: Birkhäuser; 2001.
   Google Scholar
• Bohner M , Peterson A . Advances in dynamic equations on time scales. Boston: Birkhäuser; 2003.
   Google Scholar
• Kaufmann ER , Raffoul YN . Periodic solutions for a neutral nonlinear dynamical equation on a time scale. J Math Anal Appl. 2006;319:315–325.
   Web of Science ®Google Scholar
• Fink AM . Almost periodic differential equations. Vol. 377, Lecture notes in mathematics. New York (NY): Springer-Verlag; 1974.
   Google Scholar
• Corduneanu C . Almost periodic functions. 2nd ed. New York (NY): Chelsea; 1989.
   Google Scholar
• Wang C , Agarwal RP , O’Regan D . Compactness criteria and new impulsive functional dynamic equations on time scales. Adv Differ Equ. 2016;197:1–41.
   Google Scholar