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Fractional Calculus and Applied Analysis

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Volume 22, Issue 6


Some further results of the laplace transform for variable–order fractional difference equations

Dumitru Baleanu
  • College of Mechanics and Materials State Key Laboratory of Hydrology–Water Resources and Hydraulic Engineering Hohai University, Nanjing, Jiangsu 210098, PR China
  • Department of Mathematics, Cankaya University, 06530 Balgat, Ankara, Turkey
  • Institute of Space Sciences, Magurele–Bucharest, Romania
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/ Guo–Cheng Wu
  • Data Recovery Key Laboratory of Sichuan Province College of Mathematics and Information Science Neijiang Normal University, Neijiang, 641100, PR China
  • Numerical Simulation Key Laboratory of Sichuan Province Neijiang Normal University, Neijiang, 641110, PR China
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Published Online: 2019-12-31 | DOI: https://doi.org/10.1515/fca-2019-0084


The Laplace transform is important for exact solutions of linear differential equations and frequency response analysis methods. In comparison with the continuous–time systems, less results can be available for fractional difference equations. This study provides some fundamental results of two kinds of fractional difference equations by use of the Laplace transform. Some discrete Mittag–Leffler functions are defined and their Laplace transforms are given. Furthermore, a class of variable–order and short memory linear fractional difference equations are proposed and the exact solutions are obtained.

MSC 2010: Primary 26A33; Secondary 65Q10

Key Words and Phrases: Laplace transform; fractional difference equations; variable–order; short memory

This paper is dedicated to the memory of late Professor Wen Chen


About the article

Received: 2019-07-18

Published Online: 2019-12-31

Published in Print: 2019-12-18

Citation Information: Fractional Calculus and Applied Analysis, Volume 22, Issue 6, Pages 1641–1654, ISSN (Online) 1314-2224, ISSN (Print) 1311-0454, DOI: https://doi.org/10.1515/fca-2019-0084.

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