A new fractional operator of variable order: Application in the description of anomalous diffusion

By Xiao-jun Yang, J. Machado. 2016

263 citations recorded by the source corpus.

In this paper, a new fractional operator of variable order with the use of the monotonic increasing function is proposed in sense of Caputo type. The properties in term of the Laplace and Fourier transforms are analyzed and the results for the anomalous diffusion equations of variable order are discussed. The new formulation is efficient in modeling a class of concentrations in the complex transport process.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/e650309199caf90b3e8a373a551f695a6f6769bf

How researchers see this paper

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In Applied Mathematics

1. A. Chang
2. Wen Chen
3. Yong Zhang
4. Hongguang Sun
5. Arran Fernandez
6. Dumitru Băleanu

In Modeling and Simulation

1. Yong Zhang
2. A. Chang
3. Wen Chen
4. Hongguang Sun
5. Dumitru Băleanu
6. Arran Fernandez
7. Ali H. Bhrawy
8. M. A. Zaky

In Numerical Analysis

1. A. Chang
2. Wen Chen
3. Yong Zhang
4. Hongguang Sun
5. Dumitru Băleanu
6. Arran Fernandez

Citations in the corpus

• Numerical solution of multiterm variable‐order fractional differential equations via shifted Legendre polynomials (2019, unknown): “Then we have ||u(t) − un(t)|| ≤ MHn+1 (n + 1)!√l (19)”
• A review on variable-order fractional differential equations: mathematical foundations, physical models, numerical methods and applications (2019, methodology): “In addition, the VO fractional operator has also been used in other non-local definitions with non-singular kernels, which is beyond the scope of this review [99, 127].”