An inverse problem approach to determine possible memory length of fractional differential equations
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Chuan–Yun Gu
und
Babak Shiri
Abstract
It is a fundamental problem to determine a starting point in fractional differential equations which reveals the memory length in real life modeling. This paper describes it by an inverse problem. Fixed point theorems such as Krasnoselskii’s and Schauder type’s and nonlinear alternative for single–valued mappings are presented. Through existence analysis of the inverse problem, the range of the initial value points and the memory length of fractional differential equations are obtained. Finally, three examples are demonstrated to support the theoretical results and numerical solutions are provided.
Acknowledgements
This work is financially supported by the National Natural Science Foundation of China (Grant No. 62076141), the Special Scientific Research Projects for Doctors of Sichuan University of Arts and Science (No. 2019BS009Z) and Open Research Fund Program of Data Recovery Key Laboratory of Sichuan Province (Grant No. DRN2101).
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Artikel in diesem Heft
- Frontmatter
- Editorial
- FCAA related news, events and books (FCAA–volume 24–6–2021)
- Research Paper
- Weighted fractional Hardy operators and their commutators on generalized Morrey spaces over quasi-metric measure spaces
- B-spline collocation discretizations of caputo and Riemann-Liouville derivatives: A matrix comparison
- A strong maximum principle for the fractional laplace equation with mixed boundary condition
- Difference between Riesz derivative and fractional Laplacian on the proper subset of ℝ
- Some properties of the fractal convolution of functions
- Continuous dependence of fuzzy mild solutions on parameters for IVP of fractional fuzzy evolution equations
- Discrete fractional boundary value problems and inequalities
- On the generalized fractional Laplacian
- Recent developments on the realization of fractance device
- Explicit representation of discrete fractional resolvent families in Banach spaces
- Convergence rate estimates for the kernelized predictor corrector method for fractional order initial value problems
- Inverse problems for diffusion equation with fractional Dzherbashian-Nersesian operator
- An inverse problem approach to determine possible memory length of fractional differential equations
Artikel in diesem Heft
- Frontmatter
- Editorial
- FCAA related news, events and books (FCAA–volume 24–6–2021)
- Research Paper
- Weighted fractional Hardy operators and their commutators on generalized Morrey spaces over quasi-metric measure spaces
- B-spline collocation discretizations of caputo and Riemann-Liouville derivatives: A matrix comparison
- A strong maximum principle for the fractional laplace equation with mixed boundary condition
- Difference between Riesz derivative and fractional Laplacian on the proper subset of ℝ
- Some properties of the fractal convolution of functions
- Continuous dependence of fuzzy mild solutions on parameters for IVP of fractional fuzzy evolution equations
- Discrete fractional boundary value problems and inequalities
- On the generalized fractional Laplacian
- Recent developments on the realization of fractance device
- Explicit representation of discrete fractional resolvent families in Banach spaces
- Convergence rate estimates for the kernelized predictor corrector method for fractional order initial value problems
- Inverse problems for diffusion equation with fractional Dzherbashian-Nersesian operator
- An inverse problem approach to determine possible memory length of fractional differential equations
