Some further results of the laplace transform for variable–order fractional difference equations
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Dumitru Baleanu
und
Guo–Cheng Wu
Abstract
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.
This paper is dedicated to the memory of late Professor Wen Chen
Acknowledgments
The first author (D. B.) is supported by the Scientific and Technological Research Council of Turkey (TUBTAK) (Grant No. TBAG–117F473). The second author Guo–Cheng Wu is supported by Sichuan Science and Technology Support Program (Grant No. 2018JY0120).
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© 2019 Diogenes Co., Sofia
Artikel in diesem Heft
- Frontmatter
- Editorial Note
- FCAA special issue – In memory of late professor Wen Chen (FCAA–Volume 22–6–2019)
- Survey Paper
- State-of-art survey of fractional order modeling and estimation methods for lithium-ion batteries
- An investigation on continuous time random walk model for bedload transport
- Tutorial Survey
- Porous functions
- Research Paper
- A time-space Hausdorff derivative model for anomalous transport in porous media
- High-order algorithms for riesz derivative and their applications (IV)
- Mass-conserving tempered fractional diffusion in a bounded interval
- Dispersion analysis for wave equations with fractional Laplacian loss operators
- Lagrangian solver for vector fractional diffusion in bounded anisotropic aquifers: Development and application
- Some further results of the laplace transform for variable–order fractional difference equations
- Robust stability analysis of LTI systems with fractional degree generalized frequency variables
- Discovering a universal variable-order fractional model for turbulent Couette flow using a physics-informed neural network
Artikel in diesem Heft
- Frontmatter
- Editorial Note
- FCAA special issue – In memory of late professor Wen Chen (FCAA–Volume 22–6–2019)
- Survey Paper
- State-of-art survey of fractional order modeling and estimation methods for lithium-ion batteries
- An investigation on continuous time random walk model for bedload transport
- Tutorial Survey
- Porous functions
- Research Paper
- A time-space Hausdorff derivative model for anomalous transport in porous media
- High-order algorithms for riesz derivative and their applications (IV)
- Mass-conserving tempered fractional diffusion in a bounded interval
- Dispersion analysis for wave equations with fractional Laplacian loss operators
- Lagrangian solver for vector fractional diffusion in bounded anisotropic aquifers: Development and application
- Some further results of the laplace transform for variable–order fractional difference equations
- Robust stability analysis of LTI systems with fractional degree generalized frequency variables
- Discovering a universal variable-order fractional model for turbulent Couette flow using a physics-informed neural network
