Discrete Fractional Calculus

Goodrich, Christopher S.; Peterson, Allan

doi:10.1007/978-3-319-25562-0

Cited by 505 publications

(408 citation statements)

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“…For more details about the theory of time scale calculus and the theory of quantum calculus, the reader may want to consult [1,[20][21][22].…”

Section: Preliminariesmentioning

confidence: 99%

Almost Automorphic Functions on the Quantum Time Scale and Applications

2017

Discrete Dynamics in Nature and Society

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We first propose two types of concepts of almost automorphic functions on the quantum time scale. Secondly, we study some basic properties of almost automorphic functions on the quantum time scale. Then, we introduce a transformation between functions defined on the quantum time scale and functions defined on the set of generalized integer numbers; by using this transformation we give equivalent definitions of almost automorphic functions on the quantum time scale; following the idea of the transformation, we also give a concept of almost automorphic functions on more general time scales that can unify the concepts of almost automorphic functions on almost periodic time scales and on the quantum time scale. Finally, as an application of our results, we establish the existence of almost automorphic solutions of linear and semilinear dynamic equations on the quantum time scale.

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“…For more details about the theory of time scale calculus and the theory of quantum calculus, the reader may want to consult [1,[20][21][22].…”

Section: Preliminariesmentioning

confidence: 99%

Almost Automorphic Functions on the Quantum Time Scale and Applications

2017

Discrete Dynamics in Nature and Society

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“…Author details 1 School of Mathematics and Statistics, Longdong University, Qingyang, Gansu 745000, P.R. China.…”

Section: An Examplementioning

confidence: 99%

Solvability for a discrete fractional mixed type sum-difference equation boundary value problem in a Banach space

Zhu

2016

Bound Value Probl

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“…Basic definitions and properties of fractional difference calculus were proposed by Goodrich and Peterson [3]. The developments of the theory related to discrete fractional boundary value problems were studied by many authors (see ).…”

Section: Introductionmentioning

confidence: 99%