A new fractional derivative involving the normalized sinc function without singular kernel

Abstract

In this paper, a new fractional derivative involving the normalized sinc function without singular kernel is proposed. The Laplace transform is used to find the analytical solution of the anomalous heat-diffusion problems. The comparative results between classical and fractional-order operators are presented. The results are significant in the analysis of one-dimensional anomalous heat-transfer problems.

arXiv commentKeywords: Fractional derivative, anomalous heat diffusion, integral transform, analytical solution

References in corpus (3)

• A new fractional derivative without singular kernel: Application to the modelling of the steady heat flow
• Some aspects of fractional diffusion equations of single and distributed order
• Fractional derivatives of constant and variable orders applied to anomalous relaxation models in heat-transfer problems

Cited by in corpus (1)

• On the Nonlinear $\Psi$-Hilfer Fractional Differential Equations