Fractional derivatives of constant and variable orders applied to anomalous relaxation models in heat-transfer problems

Abstract

In the present paper, we address a class of the fractional derivatives of constant and variable orders for the first time. Fractional-order relaxation equations of constants and variable orders in the sense of Caputo type are modeled from mathematical view of point. The comparative results of the anomalous relaxation among the various fractional derivatives are also given. They are very efficient in description of the complex phenomenon arising in heat transfer.

13 pages, 2 figures

References in corpus (2)

• A new fractional derivative without singular kernel: Application to the modelling of the steady heat flow
• Time-fractional derivatives in relaxation processes: a tutorial survey

Cited by in corpus (4)

• A new fractional derivative involving the normalized sinc function without singular kernel
• On the Nonlinear $\Psi$-Hilfer Fractional Differential Equations
• A new fractional derivative of variable order with non-singular kernel and fractional differential equations
• Stability Analysis of Fractional Differential Equations with Unknown Parameters