Mechanics with variable‐order differential operators

By C. Coimbra. 2003

497 citations recorded by the source corpus.

Subfields: Automotive Engineering, Control and Systems Engineering, Mechanical Engineering

View Paper: https://www.semanticscholar.org/paper/b167ea1490ec9319cf53ac2178b6cf43a1088eac

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Automotive Engineering

1. A. Chang
2. A. Aghili
3. Farzad Khane Keshi
4. Ian L Turner
5. Ali H. Bhrawy
6. Wen Chen
7. J. Chen
8. M. A. Zaky

In Control and Systems Engineering

1. Xiao-jun Yang
2. Abdon Atangana
3. Ali H. Bhrawy
4. M. A. Zaky
5. Aydin Seçer
6. Behrouz Parsa Moghaddam
7. Yong Zhang
8. A. Aghili

In Mechanical Engineering

1. A. Chang
2. A. Aghili
3. Farzad Khane Keshi
4. Ian L Turner
5. Ali H. Bhrawy
6. Wen Chen
7. J. Chen
8. M. A. Zaky

Citations in the corpus

• Numerical simulation for two-dimensional variable-order fractional nonlinear cable equation (2014, methodology): “Another important definitions of the variable-order derivative operators based on Caputo’s differential operator are proposed in [26,38].”
• Initial-boundary-value problems for the generalized multi-term time-fractional diffusion equation (2011, unknown): “One of them introduces the fractional derivatives of the variable order, i.e., the derivatives with the order that can change with the time or/and depending on the spatial coordinates (for the definitions and applications see e.g. [6] [17] [32]).”
• A variable-order time-fractional derivative model for chloride ions sub-diffusion in concrete structures (2012, background): “The definition of variable-order Caputo fractional derivative is straightforward and is written as [7]”
• A characteristic difference method for the variable-order fractional advection-diffusion equation (2013, methodology): “Coimbra [4] proposed an approximation with first-order accuracy for the variable-order differential equations.”
• A Review of Definitions for Fractional Derivatives and Integral (2014, unknown): “(17) Coimbra derivative [43–45]: Dα(x) 0 [f (x)]”
• Fractional integration and differentiation of variable order: an overview (2012, background): “However, later there appeared papers where such operators were given a certain physical meaning and they were used in applications in physics and signal processing, see for instance, [4, 5, 22, 23, 60].”
• A Physical experimental study of variable-order fractional integrator and differentiator (2011, background): “Another important definition of the variableorder derivative operators based on Caputo’s differential operator is [Coimbra (2003)]”