Bounded solutions to systems of fractional discrete equations
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Date
2022-07-19
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Mark
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De Gruyter
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Abstract
The article is concerned with systems of fractional discrete equations Delta(alpha)x(n + 1) = F-n(n, x(n), x(n - 1), ..., x(n(0))), n = n(0), n(0) + 1, ..., where n(0) is an element of Z , n is an independent variable, Delta(alpha) is an alpha-order fractional difference, alpha is an element of R, F-n : {n} x Rn-n0+1 -> R-s, S >= 1 is a fixed integer, and x : {n(0), n(0) + 1, ...} -> R-s is a dependent (unknown) variable. A retract principle is used to prove the existence of solutions with graphs remaining in a given domain for every n >= n(0), which then serves as a basis for further proving the existence of bounded solutions to a linear nonhomogeneous system of discrete equations Delta(alpha)x(n + 1) = A(n)x(n) + delta(n), n = n(0), n(0) + 1, ..., where A(n) is a square matrix and delta(n) is a vector function. Illustrative examples accompany the statements derived, possible generalizations are discussed, and open problems for future research are formulated as well.
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Advances in Nonlinear Analysis. 2022, vol. 11, issue 1, p. 1614-1630.
https://www.degruyter.com/document/doi/10.1515/anona-2022-0260/html
https://www.degruyter.com/document/doi/10.1515/anona-2022-0260/html
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Peer-reviewed
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en