Existence of weighted bounded solutions for nonlinear discrete-time fractional equations

References

• Abdeljawad T. On Riemann and Caputo fractional differences. Comput Math Appl. 2011;62:1602–1611. doi: 10.1016/j.camwa.2011.03.036
   Web of Science ®Google Scholar
• Abdeljawad T, Atici FM. On the definitions of nabla fractional operators. Abstr Appl Anal. 2012;2012:1–13.
   Google Scholar
• Atici FM, Eloe PW. A transform method in discrete fractional calculus. Int J Differ Equ. 2007;2(2):165–176.
   Google Scholar
• Atici FM, Eloe PW. Initial value problems in discrete fractional calculus. Proc Amer Math Soc. 2009;137(3):981–989. doi: 10.1090/S0002-9939-08-09626-3
   Web of Science ®Google Scholar
• Lizama C, Murillo-Arcila M. Maximal regularity in lp spaces for discrete time fractional shifted equations. J Differ Equ. 2017;263(6):3175–3196. doi: 10.1016/j.jde.2017.04.035
   Web of Science ®Google Scholar
• Atici FM, Sengül S. Modeling with fractional difference equations. J Math Anal Appl. 2010;369:1–9. doi: 10.1016/j.jmaa.2010.02.009
   Web of Science ®Google Scholar
• Baleanu D, Diethelm K, Scalas E, et al. Fractional calculus: models and numerical methods. London: World Scientific; 2012.
   Google Scholar
• Bateman H. The control of an elastic fluid. Bull Amer Math Soc. 1945;51:601–646. doi: 10.1090/S0002-9904-1945-08413-4
   Web of Science ®Google Scholar
• Fu X, Li M. Spatial dynamics for lattice difference equations with a shifting habitat. J Differ Equ. 2015;259:1957–1989.
   Web of Science ®Google Scholar
• Li Z-M, Chang X-H, Mathiyalagan K, et al. Robust energy-to-peak filtering for discrete-time nonlinear systems with measurement quantization. Signal Process. 2017;139(1):1339–1351.
   Google Scholar
• Mallet-Paret J. The global structure of travelling waves in spatiallydiscrete dynamical systems. J Dyn Differ Equ. 1999;11(1):49–127. doi: 10.1023/A:1021841618074
   Google Scholar
• Borrelli F, Baotic M, Bemporad A, et al. Dynamic programming for constrained optimal control of discrete-time linear hybrid systems. Automatica. 2005;41:1709–1721. doi: 10.1016/j.automatica.2005.04.017
   Web of Science ®Google Scholar
• Simsek EH, Gulec E, Kavustu H. Application of Kalman filter to determination of coal liquefaction mechanisms using discrete time models. Fuel. 2017;207(1):814–820. doi: 10.1016/j.fuel.2017.06.004
   Google Scholar
• Tarasov VE. Fractional-order difference equations for physical lattices and some applications. J Math Phys. 2015;56(10):1–19. doi: 10.1063/1.4933028
   Web of Science ®Google Scholar
• Tarasov VE. Fractional Liouville equation on lattice phase-space. Phys A. 2015;421:330–342. doi: 10.1016/j.physa.2014.11.031
   Web of Science ®Google Scholar
• Tarasova VV, Tarasov VE. Logistic map with memory from economic model. Chaos Solitons Fractals. 2017;95:84–91. doi: 10.1016/j.chaos.2016.12.012
   Web of Science ®Google Scholar
• Cuesta E, Lubich C, Palencia C. Convolution quadrature time discretization of fractional diffusion-wave equations. Math. Comput. 2006;75(254):673–696. doi: 10.1090/S0025-5718-06-01788-1
   Web of Science ®Google Scholar
• Sanz-Serna JM. A numerical method for partial integro-differential equation. SIAM J Numer Anal. 1988;25:319–327. doi: 10.1137/0725022
   Web of Science ®Google Scholar
• Lizama C. ℓp-maximal regularity for fractional difference equations on UMD spaces. Math Nach. 2015;288(1718):2079–2092. doi: 10.1002/mana.201400326
   Google Scholar
• Lizama C, Murillo-Arcila M. ℓp-maximal regularity for a class of fractional difference equations on UMD spaces: the case 1<α≤2. Banach J Math Anal. 2017;11(1):188–206. doi: 10.1215/17358787-3784616
   Web of Science ®Google Scholar
• Lizama C, Velasco MP. Weighted bounded solutions for a class of nonlinear fractional equations. Fract Calc Appl Anal. 2016;19(4):1010–1030. doi: 10.1515/fca-2016-0055
   Web of Science ®Google Scholar
• Amini S, Sloan IH. Collocation method for second kind integral equations with non-compact operators. J Int Equ Appl. 1989;2(1):1–30. doi: 10.1216/JIE-1989-2-1-1
   Google Scholar
• Chojnacki W. On operator-valued cosine sequences on UMD spaces. Studia Math. 2010;199(3):267–278. doi: 10.4064/sm199-3-4
   Web of Science ®Google Scholar
• Agarwal RP, Cuevas C, Lizama C. Regularity of difference equations on banach spaces. Cham: Springer-Verlag; 2014.
   Google Scholar
• Lizama C. The Poisson distribution, abstract fractional difference equations, and stability. Proc Amer Math Soc. 2017;145(9):3809–3827. doi: 10.1090/proc/12895
   Web of Science ®Google Scholar
• Zygmund A. Trigonometric Series. 2nd ed. New York: Cambridge University Press; 1959.
   Google Scholar
• Kreyszig E. Introductory functional analysis with applications. John Wiley & Sons: New York; 1989.
   Google Scholar
• Prudnikov AP, Brychkov YA, Marichev OI. Integrals and series. Amsterdam: Gordon and Breach Science Publishers; 1986.
   Google Scholar