Fractional impulsive differential equations: Exact solutions, integral equations and short memory case
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Guo–Cheng Wu
Abstract
Fractional impulsive differential equations are revisited first. Some fundamental solutions of linear cases are given in this study. One straightforward technique without using integral equation is adopted to obtain exact solutions which are given by use of piecewise functions. Furthermore, a class of short memory fractional differential equations is proposed and the variable case is discussed. Mittag–Leffler solutions with impulses are derived which both satisfy the equations and impulsive conditions, respectively.
Acknowledgments
This paper is dedicated to the memory of the late Professor Wen Chen (Hohai University).
The first author thanks for Professor Chen’s encouragement in studies of fractional differential equations. The third author had many fruitful discussions with Professor Chen during the last twelve years and organized two international conferences together. The authors also thank the referees’ sincere and helpful suggestions to improve this study. The second author helps with future work of the conclusion part. The first author was financially 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 related news, events and books (FCAA–volume 22–1–2019)
- Survey Paper
- Ranking the scientific output of researchers in fractional calculus
- A review on variable-order fractional differential equations: mathematical foundations, physical models, numerical methods and applications
- Research Paper
- From power laws to fractional diffusion processes with and without external forces, the non direct way
- Homogeneous robin boundary conditions and discrete spectrum of fractional eigenvalue problem
- The numerical algorithms for discrete Mittag-Leffler functions approximation
- New interpretation of fractional potential fields for robust path planning
- Stable distributions and green’s functions for fractional diffusions
- Fractional calculus in economic growth modelling of the group of seven
- Relationship between controllability and observability of standard and fractional different orders discrete-time linear system
- Optimal control of linear systems of arbitrary fractional order
- Fractional impulsive differential equations: Exact solutions, integral equations and short memory case
- Fractional-order modelling and parameter identification of electrical coils
- Fractional-order value identification of the discrete integrator from a noised signal. part I
Artikel in diesem Heft
- Frontmatter
- Editorial Note
- FCAA related news, events and books (FCAA–volume 22–1–2019)
- Survey Paper
- Ranking the scientific output of researchers in fractional calculus
- A review on variable-order fractional differential equations: mathematical foundations, physical models, numerical methods and applications
- Research Paper
- From power laws to fractional diffusion processes with and without external forces, the non direct way
- Homogeneous robin boundary conditions and discrete spectrum of fractional eigenvalue problem
- The numerical algorithms for discrete Mittag-Leffler functions approximation
- New interpretation of fractional potential fields for robust path planning
- Stable distributions and green’s functions for fractional diffusions
- Fractional calculus in economic growth modelling of the group of seven
- Relationship between controllability and observability of standard and fractional different orders discrete-time linear system
- Optimal control of linear systems of arbitrary fractional order
- Fractional impulsive differential equations: Exact solutions, integral equations and short memory case
- Fractional-order modelling and parameter identification of electrical coils
- Fractional-order value identification of the discrete integrator from a noised signal. part I
