The Fading Memory Formalism with Mittag-Leffler-Type Kernels as A Generator of Non-Local Operators

Abstract

Transient heat conduction problems are systematically applied to the fading memory formalism with different Mittag-Leffler-type memory kernels. With such an approach, using various memories naturally results in definitions of various fractional operators. Six examples are given and interpreted from a common perspective, covering the most well-liked versions of the Mittag-Leffler function. The fading memory approach was used as a template and demonstrated that, if the constitutive equations are correctly built, it is also possible to directly determine where the hereditary terms are located in the models.

Keywords

• fading memory formalism
• heat conduction
• Mittag-Leffler functions
• memory kernels
• fractional derivatives