Existence of (N, λ)-periodic solutions for sbstract fractional difference equations

We establish sufficient conditions for the existence and uniqueness of (N,λ)-periodic solutions for the following abstract model: Δαu(n) = Au(n + 1) + f(n, u(n)), n ∈ Z, where 0 < α ≤ 1, A is a closed linear operator defined in a Banach space X, Δα denotes the fractional difference operator in th...

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Autores:
Dıaz, Stiven
Lizama, Carlos
Álvarez, Edgardo
Tipo de recurso:
Article of journal
Fecha de publicación:
2022
Institución:
Corporación Universidad de la Costa
Repositorio:
REDICUC - Repositorio CUC
Idioma:
eng
OAI Identifier:
oai:repositorio.cuc.edu.co:11323/9272
Acceso en línea:
https://hdl.handle.net/11323/9272
https://doi.org/10.1007/s00009-021-01964-6
https://repositorio.cuc.edu.co/
Palabra clave:
(N,λ)-periodic solutions
Banach space
Fractional difference operator
Subordination
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embargoedAccess
License
Atribución 4.0 Internacional (CC BY 4.0)
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repository_id_str
dc.title.eng.fl_str_mv Existence of (N, λ)-periodic solutions for sbstract fractional difference equations
title Existence of (N, λ)-periodic solutions for sbstract fractional difference equations
spellingShingle Existence of (N, λ)-periodic solutions for sbstract fractional difference equations
(N,λ)-periodic solutions
Banach space
Fractional difference operator
Subordination
title_short Existence of (N, λ)-periodic solutions for sbstract fractional difference equations
title_full Existence of (N, λ)-periodic solutions for sbstract fractional difference equations
title_fullStr Existence of (N, λ)-periodic solutions for sbstract fractional difference equations
title_full_unstemmed Existence of (N, λ)-periodic solutions for sbstract fractional difference equations
title_sort Existence of (N, λ)-periodic solutions for sbstract fractional difference equations
dc.creator.fl_str_mv Dıaz, Stiven
Lizama, Carlos
Álvarez, Edgardo
dc.contributor.author.spa.fl_str_mv Dıaz, Stiven
Lizama, Carlos
Álvarez, Edgardo
dc.subject.proposal.eng.fl_str_mv (N,λ)-periodic solutions
Banach space
Fractional difference operator
Subordination
topic (N,λ)-periodic solutions
Banach space
Fractional difference operator
Subordination
description We establish sufficient conditions for the existence and uniqueness of (N,λ)-periodic solutions for the following abstract model: Δαu(n) = Au(n + 1) + f(n, u(n)), n ∈ Z, where 0 < α ≤ 1, A is a closed linear operator defined in a Banach space X, Δα denotes the fractional difference operator in the Weyl-like sense, and f satisfies appropriate conditions.
publishDate 2022
dc.date.accessioned.none.fl_str_mv 2022-06-21T15:33:52Z
dc.date.available.none.fl_str_mv 2022-06-21T15:33:52Z
2023-01-30
dc.date.issued.none.fl_str_mv 2022-01-30
dc.type.spa.fl_str_mv Artículo de revista
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dc.identifier.citation.spa.fl_str_mv Alvarez, E., Díaz, S. & Lizama, C. Existence of (N,λ)-Periodic Solutions for Abstract Fractional Difference Equations. Mediterr. J. Math. 19, 47 (2022). https://doi.org/10.1007/s00009-021-01964-6
dc.identifier.issn.spa.fl_str_mv 1660-5446
dc.identifier.uri.spa.fl_str_mv https://hdl.handle.net/11323/9272
dc.identifier.url.spa.fl_str_mv https://doi.org/10.1007/s00009-021-01964-6
dc.identifier.doi.spa.fl_str_mv 10.1007/s00009-021-01964-6
dc.identifier.eissn.spa.fl_str_mv 1660-5454
dc.identifier.instname.spa.fl_str_mv Corporación Universidad de la Costa
dc.identifier.reponame.spa.fl_str_mv REDICUC - Repositorio CUC
dc.identifier.repourl.spa.fl_str_mv https://repositorio.cuc.edu.co/
identifier_str_mv Alvarez, E., Díaz, S. & Lizama, C. Existence of (N,λ)-Periodic Solutions for Abstract Fractional Difference Equations. Mediterr. J. Math. 19, 47 (2022). https://doi.org/10.1007/s00009-021-01964-6
1660-5446
10.1007/s00009-021-01964-6
1660-5454
Corporación Universidad de la Costa
REDICUC - Repositorio CUC
url https://hdl.handle.net/11323/9272
https://doi.org/10.1007/s00009-021-01964-6
https://repositorio.cuc.edu.co/
dc.language.iso.none.fl_str_mv eng
language eng
dc.relation.ispartofjournal.spa.fl_str_mv Mediterranean Journal of Mathematics
dc.relation.references.spa.fl_str_mv [1] Abadias, L., Miana, P.: A subordination principle on Wright functions and regularized resolvent families. J. Funct. Spaces 2314–889 (2015)
[2] Abadias, L., Lizama, C.: Almost automorphic mild solutions to fractional partial difference–differential equations. Appl. Anal. 95(6), 1347–1369 (2016)
[3] Abadias, L., Lizama, C., Miana, P.J., Velasco, M.P.: Ces´aro sums and algebra homomorphisms of bounded operators. Israel J. Math. 216(1), 471–505 (2016)
[4] Abdeljawad, T., Banerjee, S., Wu, G.C.: Discrete tempered fractional calculus for new chaotic systems with short memory and image encryption. Optik. 218, 163698 (2020)
[5] Agaoglou, M., Feˇckan, M., Panagiotidou, A.: Existence and uniqueness of (ω, c)-periodic solutions of semilinear evolution equations. Int. J. Dyn. Syst. Differ. Equ. 10(2), 149–166 (2020)
[6] Alvarez, E., D´ıaz, S., Lizama, C.: On the existence and uniqueness of (N,λ)- periodic solutions to a class of Volterra difference equations. Adv. Differ. Equ. 105 (2019)
[7] E. Alvarez, S. D´ıaz, C. Lizama. C-Semigroups, subordination principle and the L´evy α-stable distribution on discrete time. Commun. Contemp. Math. (to appear) https://doi.org/10.1142/S0219199720500637
[8] Alvarez, E., Castillo, S., Pinto, M.: (ω, c)-pseudo periodic functions, first order Cauchy problem and Lasota–Wazewska model with ergodic and unbounded oscillating production of red cells. Bound. Value Probl. 2019, 106 (2019). https:// doi.org/10.1186/s13661-019-1217-x
[9] Alvarez, E., Castillo, S., Pinto, M.: (ω, c)-asymptotically periodic functions, first-oerder Cauchy problem, and Lasota–Wazewska model with unbounded oscillating production of red cells. Math. Method. Appl. Sci. 43(1), 305–319 (2020)
[10] Alvarez, E., G´omez, A., Pinto, M.: (ω, c)-periodic functions and mild solutions to abstract fractional integro-differential equations. Electr. J. Qual. Th. Diff. Equ. 16, 1–8 (2018)
[11] Goodrich, C., Lizama, C.: A transference principle for nonlocal operators using a convolutional approach: fractional monotonicity and convexity. Isr. J. Math. 236, 533–589 (2020)
[12] He, J.W., Lizama, C., Zhou, Y.: The Cauchy problem for discrete-time fractional evolution equations. J. Comput. Appl. Math. 370, 112683 (2020)
[13] Huang, L.L., Park, J.H., Wu, G.C., Mo, Z.W.: Variable-order fractional discrete-time recurrent neural networks. J. Comp. Appl. Math. 370, 112633 (2020)
[14] Huang, L.L., Wu, G.C., Baleanu, D., Wang, H.Y.: Discrete fractional calculus for interval-valued systems. Fuzzy Sets Syst. 404, 141–158 (2021)
[15] Khalladi, M., Kosti´c, M., Rahmani, A., Velinov D.: (ω, c)-almost periodic type functions and applications. (2020) hal.archives-ouvertes.fr
[16] Khalladi, M., Rahmani, A.: (ω, c)-Pseudo almost periodic distributions. Nonauton. Dyn. Syst. 7(1) (2020)
[17] Kosti´c, M.: Multidimensional (ω, c)- almost periodic type functions and applications. hal.archives-ouvertes.fr
[18] Kosti´c, M., Fedorov, V.E.: Asymptotically (ω, c)-almost periodic type solutions of abstract degenerate non-scalar Volterra equations. Chelyabinsk Phys. Math. J. 5(4), 415–427 (2020)
[19] Liu, K., Wang, J., O’Regan, D., Feˇckan, M.: A new class of (ω, c)-periodic non-instantaneous impulsive differential equations. Mediterr. J. Math. 17, 155 (2020)
[20] Lizama, C.: p-maximal regularity for fractional difference equations on UMD spaces. Math. Nach. 288(17/18), 2079–2092 (2015)
[21] Lizama, C.: The Poisson distribution, abstract fractional difference equations, and stability. Proc. Am. Math. Soc. 145(9), 3809–3827 (2017)
[22] Lizama, C., Murillo, M.: Maximal regularity in lp spaces for discrete time fractional shifted equations. J. Differ. Equ. 263(6), 3175–3196 (2017)
[23] Lizama, C., Ponce, R.: Solutions of abstract integro–differential equations via Poisson transformation. Math. Method Appl. Sci. 44(3), 2495–2505 (2021)
[24] Lizama, C., Velasco, M.P.: Weighted bounded solutions for a class of nonlinear fractional equations. Fract. Calc. Appl. Anal. 19(4), 1010–1030 (2016)
[25] Lunardi. A.: Analytic semigroups and optimal regularity in parabolic problems. PNLDE, vol 16. Birkh¨auser Verlag, Basel (1995)
[26] Mophou, G., N’Gu´er´ekata, G.: An existence result of (ω, c)-periodic mild solutions to some fractional differential equation. hal.archives-ouvertes.fr
[27] Mozyrska, D., Wyrwas, M.: The Z-transform method and delta type fractional difference operators, Disc. Dyn. Nat. Soc. Art. ID 852734, 12, 1026-1226 (2015). https://doi.org/10.1155/2015/852734
[28] Podlubny, I.: Fractional Differential Equations, Vol. 198, Academic Press, 340 (1999)
[29] Prudnikov, A.P., Brychkov, A.Y., Marichev, O.I.: Integrals and Series. Elementary Functions, vol. 1. Gordon and Breach Science Publishers, New York (1986)
[30] Wang, J., Ren, L., Zhou, Y.: (ω, c)-periodic solutions for time varying impulsive differential equations. Adv. Differ. Equ. 259 (2019)
[31] Wu, G.C., Baleanu, D., Bai, Y.R.: Discrete fractional masks and their applications to image enhancement. Appl. Eng. Life Soc. Sci. Part B, 261–270 (2019)
[32] Wu, G.C., Baleanu, D., Luo, W.H.: Lyapunov functions for Riemann–Liouvillelike fractional difference equations. Appl. Math. Comp. 314, 228–236 (2017)
[33] Zygmund, A.: Trigonometric Series, vol. I, 2nd edn. Cambridge University Press, New York (1959)
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spelling Dıaz, StivenLizama, CarlosÁlvarez, Edgardo2022-06-21T15:33:52Z2023-01-302022-06-21T15:33:52Z2022-01-30Alvarez, E., Díaz, S. & Lizama, C. Existence of (N,λ)-Periodic Solutions for Abstract Fractional Difference Equations. Mediterr. J. Math. 19, 47 (2022). https://doi.org/10.1007/s00009-021-01964-61660-5446https://hdl.handle.net/11323/9272https://doi.org/10.1007/s00009-021-01964-610.1007/s00009-021-01964-61660-5454Corporación Universidad de la CostaREDICUC - Repositorio CUChttps://repositorio.cuc.edu.co/We establish sufficient conditions for the existence and uniqueness of (N,λ)-periodic solutions for the following abstract model: Δαu(n) = Au(n + 1) + f(n, u(n)), n ∈ Z, where 0 < α ≤ 1, A is a closed linear operator defined in a Banach space X, Δα denotes the fractional difference operator in the Weyl-like sense, and f satisfies appropriate conditions.15 páginasapplication/pdfengBirkhauser Verlag BaselSwitzerlandAtribución 4.0 Internacional (CC BY 4.0)© The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022https://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/embargoedAccesshttp://purl.org/coar/access_right/c_f1cfExistence of (N, λ)-periodic solutions for sbstract fractional difference equationsArtículo de revistahttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1Textinfo:eu-repo/semantics/articlehttp://purl.org/redcol/resource_type/ARThttp://purl.org/coar/version/c_970fb48d4fbd8a85https://link.springer.com/article/10.1007/s00009-021-01964-6#citeasMediterranean Journal of Mathematics[1] Abadias, L., Miana, P.: A subordination principle on Wright functions and regularized resolvent families. J. Funct. Spaces 2314–889 (2015)[2] Abadias, L., Lizama, C.: Almost automorphic mild solutions to fractional partial difference–differential equations. Appl. Anal. 95(6), 1347–1369 (2016)[3] Abadias, L., Lizama, C., Miana, P.J., Velasco, M.P.: Ces´aro sums and algebra homomorphisms of bounded operators. Israel J. Math. 216(1), 471–505 (2016)[4] Abdeljawad, T., Banerjee, S., Wu, G.C.: Discrete tempered fractional calculus for new chaotic systems with short memory and image encryption. Optik. 218, 163698 (2020)[5] Agaoglou, M., Feˇckan, M., Panagiotidou, A.: Existence and uniqueness of (ω, c)-periodic solutions of semilinear evolution equations. Int. J. Dyn. Syst. Differ. Equ. 10(2), 149–166 (2020)[6] Alvarez, E., D´ıaz, S., Lizama, C.: On the existence and uniqueness of (N,λ)- periodic solutions to a class of Volterra difference equations. Adv. Differ. Equ. 105 (2019)[7] E. Alvarez, S. D´ıaz, C. Lizama. C-Semigroups, subordination principle and the L´evy α-stable distribution on discrete time. Commun. Contemp. Math. (to appear) https://doi.org/10.1142/S0219199720500637[8] Alvarez, E., Castillo, S., Pinto, M.: (ω, c)-pseudo periodic functions, first order Cauchy problem and Lasota–Wazewska model with ergodic and unbounded oscillating production of red cells. Bound. Value Probl. 2019, 106 (2019). https:// doi.org/10.1186/s13661-019-1217-x[9] Alvarez, E., Castillo, S., Pinto, M.: (ω, c)-asymptotically periodic functions, first-oerder Cauchy problem, and Lasota–Wazewska model with unbounded oscillating production of red cells. Math. Method. Appl. Sci. 43(1), 305–319 (2020)[10] Alvarez, E., G´omez, A., Pinto, M.: (ω, c)-periodic functions and mild solutions to abstract fractional integro-differential equations. Electr. J. Qual. Th. Diff. Equ. 16, 1–8 (2018)[11] Goodrich, C., Lizama, C.: A transference principle for nonlocal operators using a convolutional approach: fractional monotonicity and convexity. Isr. J. Math. 236, 533–589 (2020)[12] He, J.W., Lizama, C., Zhou, Y.: The Cauchy problem for discrete-time fractional evolution equations. J. Comput. Appl. Math. 370, 112683 (2020)[13] Huang, L.L., Park, J.H., Wu, G.C., Mo, Z.W.: Variable-order fractional discrete-time recurrent neural networks. J. Comp. Appl. Math. 370, 112633 (2020)[14] Huang, L.L., Wu, G.C., Baleanu, D., Wang, H.Y.: Discrete fractional calculus for interval-valued systems. Fuzzy Sets Syst. 404, 141–158 (2021)[15] Khalladi, M., Kosti´c, M., Rahmani, A., Velinov D.: (ω, c)-almost periodic type functions and applications. (2020) hal.archives-ouvertes.fr[16] Khalladi, M., Rahmani, A.: (ω, c)-Pseudo almost periodic distributions. Nonauton. Dyn. Syst. 7(1) (2020)[17] Kosti´c, M.: Multidimensional (ω, c)- almost periodic type functions and applications. hal.archives-ouvertes.fr[18] Kosti´c, M., Fedorov, V.E.: Asymptotically (ω, c)-almost periodic type solutions of abstract degenerate non-scalar Volterra equations. Chelyabinsk Phys. Math. J. 5(4), 415–427 (2020)[19] Liu, K., Wang, J., O’Regan, D., Feˇckan, M.: A new class of (ω, c)-periodic non-instantaneous impulsive differential equations. Mediterr. J. Math. 17, 155 (2020)[20] Lizama, C.: p-maximal regularity for fractional difference equations on UMD spaces. Math. Nach. 288(17/18), 2079–2092 (2015)[21] Lizama, C.: The Poisson distribution, abstract fractional difference equations, and stability. Proc. Am. Math. Soc. 145(9), 3809–3827 (2017)[22] Lizama, C., Murillo, M.: Maximal regularity in lp spaces for discrete time fractional shifted equations. J. Differ. Equ. 263(6), 3175–3196 (2017)[23] Lizama, C., Ponce, R.: Solutions of abstract integro–differential equations via Poisson transformation. Math. Method Appl. Sci. 44(3), 2495–2505 (2021)[24] Lizama, C., Velasco, M.P.: Weighted bounded solutions for a class of nonlinear fractional equations. Fract. Calc. Appl. Anal. 19(4), 1010–1030 (2016)[25] Lunardi. A.: Analytic semigroups and optimal regularity in parabolic problems. PNLDE, vol 16. Birkh¨auser Verlag, Basel (1995)[26] Mophou, G., N’Gu´er´ekata, G.: An existence result of (ω, c)-periodic mild solutions to some fractional differential equation. hal.archives-ouvertes.fr[27] Mozyrska, D., Wyrwas, M.: The Z-transform method and delta type fractional difference operators, Disc. Dyn. Nat. Soc. Art. ID 852734, 12, 1026-1226 (2015). https://doi.org/10.1155/2015/852734[28] Podlubny, I.: Fractional Differential Equations, Vol. 198, Academic Press, 340 (1999)[29] Prudnikov, A.P., Brychkov, A.Y., Marichev, O.I.: Integrals and Series. Elementary Functions, vol. 1. Gordon and Breach Science Publishers, New York (1986)[30] Wang, J., Ren, L., Zhou, Y.: (ω, c)-periodic solutions for time varying impulsive differential equations. Adv. Differ. Equ. 259 (2019)[31] Wu, G.C., Baleanu, D., Bai, Y.R.: Discrete fractional masks and their applications to image enhancement. Appl. Eng. Life Soc. Sci. Part B, 261–270 (2019)[32] Wu, G.C., Baleanu, D., Luo, W.H.: Lyapunov functions for Riemann–Liouvillelike fractional difference equations. Appl. Math. Comp. 314, 228–236 (2017)[33] Zygmund, A.: Trigonometric Series, vol. I, 2nd edn. 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