Existence of $$(N,\lambda )$$-Periodic Solutions for Abstract Fractional Difference Equations

Abstract

We establish sufficient conditions for the existence and uniqueness of (N, λ)-periodic solutions for the following abstract model:where 0 < α ≤ 1, A is a closed linear operator defined in a Banach space X, Δ α denotes the fractional difference operator in the Weyl-like sense, and f satisfies appropriate conditions.

Generalized almost periodic solutions of Volterra difference equations

“…Fractional analogues of u(k + 1) = Au(k) + f (k). In [2], E. Alvarez, S. Díaz and C. Lizama have recently analyzed the existence and uniqueness of (N, λ)-periodic solutions for the abstract fractional difference equation…”

Generalized ρ-Almost Periodic Sequences and Applications

“…Discrete fractional calculus is a very attractive field of applied mathematics and computation, which is incredibly important in the modeling of various phenomena concerning interval-valued systems, chaotic systems with short memory and image encryption and discrete-time recurrent neural networks. In the recent research article [46], E. Alvarez, S. Díaz and C. Lizama have analyzed the existence and uniqueness of (N, λ)-periodic solutions for the abstract fractional difference equation…”

The role of stewards at sports events in the Republic of Serbia

“…Discrete fractional calculus, discrete fractional equations and discrete Volterra equations have received much attention recently, as well (cf. the monographs [3] by S. Abbas et al, [5] by M. H. Annaby, Z. S. Mansour, [14] by R. A. C. Ferreira, [17] by C. Goodrich, A. C. Peterson and the research articles [1,2,4,6,7,8,10,12], [13,16,18,19,20,33,35,36] for some recent results obtained in this direction). Discrete fractional calculus is incredibly important in modeling of various real phenomena appearing in the theories of neural networks, complex dynamic systems, frequency response analysis, image processing and interval-valued systems, e.g..…”

“…where A is a multivalued linear operator on a complex Banach space (X, • ), 0 < α ≤ 1 and ∆ α W u(k) denotes the Weyl fractional difference operator of order α; concerning the existence and uniqueness of almost periodic solutions and almost automorphic solutions of the abstract fractional difference equation (1.1) in which A = A is a bounded linear operator, we would like to mention here the important research articles of C. Lizama and his co-authors [1,2,4,33]. Further on, in our recent research article [31], we have analyzed the existence and uniqueness of asymptotically almost periodic solutions of the following abstract Volterra difference inclusion…”