Some new asymptotic properties on solutions to fractional evolution equations in Banach spaces

References

• Bloch F. Über die quantenmechanik der elektronen in kristallgittern. Z Phys. 1929;52:555–600.
   Google Scholar
• Ren SY. Electronic states in crystals of finite size: quantum confinement of Bloch waves. New York: Springer; 2006.
   Google Scholar
• Hasler MF, N'Guérékata GM. Bloch-periodic functions and some applications. Nonlinear Stud. 2014;21:21–30.
   Google Scholar
• Kostić M, Velinov D. Asymptotically Bloch-periodic solutions of abstract fractional nonlinear differential inclusions with piecewise constant argument. Funct Anal Approx Comput. 2017;9:27–36.
   Google Scholar
• Chang YK, Wei Y. S-asymptotically Bloch type periodic solutions to some semi-linear evolution equations in Banach spaces. Acta Math Sci. 2021;41:413–425.
   Web of Science ®Google Scholar
• Chang YK, Wei Y. Pseudo S-asymptotically Bloch type periodicity with applications to some evolution equations. Z Anal Anwend. 2021;40:33–50.
   Web of Science ®Google Scholar
• Henríquez HR, Pierri M, Táboas P. On S-asymptotically ω-periodic functions on Banach spaces and applications. J Math Anal Appl. 2008;343:1119–1130.
   Web of Science ®Google Scholar
• Pierri M. On S-asymptotically ω-periodic functions and applications. Nonliner Anal. 2012;75:651–661.
   Web of Science ®Google Scholar
• Pierri M, Rolnik V. On pseudo S-asymptotically periodic functions. Bull Aust Math Soc. 2013;87:238–254.
   Web of Science ®Google Scholar
• Alvarez E, Gomez A, Pinto M. (ω,c)-periodic functions and mild solution to abstract fractional integro-differential equations. Electron J Qual Theory Differ Equ. 2018;2018. 8pp.
   Google Scholar
• Chang YK, N'Guérékata GM, Ponce R. Bloch-type periodic functions: theory and their applications to evolution equations, to appear in Ser Concrete Appl Math. Singapore: World Scientific.
   Google Scholar
• Chaouchi B, Kostić M, Pilipovic S, et al. Semi-Bloch periodic functions, semi-anti-periodic functions and applications. Chel Phys Math J. 2020;5:243–255.
   Google Scholar
• Kéré M, N'Guérékata GM, Oueama-Guengai ER. An existence result of (ω,c)-almost periodic mild solutions to some fractional differential equation. PanAm Math J. 2021;31:11–20.
   Google Scholar
• Khalladi MT, Kostic M, Rahmani A, et al. On semi-c-periodic functions. J Math. 2021;Article ID 6620625.
   PubMed Web of Science ®Google Scholar
• Mophou G, N'Guérékata GM. An existence result of (ω,c)-periodic mild solutions to some fractional differential equation. Nonlinear Stud. 2020;27:167–175.
   Google Scholar
• Cuevas C, Lizama C. Almost automorphic solutions to a class of semilinear fractional differential equations. Appl Math Lett. 2008;21:1315–1319.
   Web of Science ®Google Scholar
• Agarwal RP, de Andrade B, Cuevas C. Weighted pseudo-almost periodic solutions of class of semilinear fractional differential equations. Nonlinear Anal RWA. 2010;11:3532–3554.
   Web of Science ®Google Scholar
• Agarwal RP, Cuevas C, Soto H. Pseudo-almost periodic solutions of a class of semilinear fractional differential equations. J Appl Math Comput. 2011;37:625–634.
   Google Scholar
• Cao J, Yang Q, Huang Z. Existence of anti-periodic mild solutions for a class of semilinear fractional differential equations. Commun Nonlinear Sci Numer Simul. 2012;17:277–283.
   Web of Science ®Google Scholar
• Chang YK, Zhang R, N'Guérékata GM. Weighted pseudo almost automorphic mild solutions to fractional differential equations. Comput Math Appl. 2012;64:3160–3170.
   Web of Science ®Google Scholar
• Brindle D, N'Guérékata GM. S-asymptotically ω-periodic mild solutions to fractional differential equations. Electron J Differ Equ. 2020;2020(30):1–12.
   Google Scholar
• Chang YK, Ponce R. Mild solutions for a multi-term fractional differential equation via resolvent operators. AIMS Math. 2021;6:2398–2417.
   Web of Science ®Google Scholar
• Abbas S, Benchohra M, N'Guérékata GM. Topics in fractional differential equations. New York: Springer; 2012.
   Google Scholar
• Cui N, Sun HR. Existence and multiplicity results for the fractional Schródinger equations with indefinite potentials. Appl Anal. 2021;100:1198–1212.
   Web of Science ®Google Scholar
• Kostić M. Almost periodic and almost automorphic solutions to integro-differential equations. Berlin: W. de Gruyter; 2019.
   Google Scholar
• Oueama-Guengai ER, N'Guérékata GM. On S-asymptotically ω-periodic and Bloch periodic mild solutions to some fractional differential equations in abstract spaces. Math Meth Appl Sci. 2018;41:9116–9122.
   Web of Science ®Google Scholar
• Wang G. Twin iterative positive solutions of fractional q-difference Schrödinger equations. Appl Math Lett. 2018;76:103–109.
   Web of Science ®Google Scholar
• Wang G, Ren X, Bai Z, et al. Radial symmetry of standing waves for nonlinear fractional Hardy–Schrödinger equation. Appl Math Lett. 2019;96:131–137.
   Web of Science ®Google Scholar
• Zhou Y, Wang J, Zhang L. Basic theory of fractional differential equations. Singapore: World Scientific; 2016.
   Google Scholar
• Zhou Y. Fractional evolution equations and inclusions: analysis and control. New York: Elsevier; 2016.
   Google Scholar
• Xia Z, Wang D, Wen CF, et al. Pseudo asymptotically periodic mild solutions of semilinear functional integro-differential equations in Banach spaces. Math Meth Appl Sci. 2017;40:7333–7355.
   Web of Science ®Google Scholar
• Yang M, Wang QR. Pseudo asymptotically periodic solutions for fractional integro-differential neutral equations. Sci China Math. 2019;62:1705–1718.
   Web of Science ®Google Scholar
• Alvarez E, Castillo S, Pinto M. (ω,c)-Pseudo periodic functions first order Cauchy problem and Lasota–Wasewska model with ergodic and unbounded oscillating production of red cells. Bound Value Prob. 2019;106:20pp..
   Google Scholar
• Ponce R. Existence of mild solutions to nonlocal fractional Cauchy problems via compactness. Abstr Appl Anal. 2016. Art. ID 4567092, 15 pp.
   Google Scholar
• Ponce R. Asymptotic behavior of mild solutions to fractional Cauchy problems in Banach spaces. Appl Math Lett. 2020;105:106322.
   Web of Science ®Google Scholar
• Henríquez HR, Lizama C. Compact almost automorphic solutions to integral equations with infinite delay. Nonlinear Anal. 2009;71:6029–6037.
   Web of Science ®Google Scholar
• Granas A, Dugundji J. Fixed point theory. New York: Springer; 2003.
   Google Scholar