Fractional Newton cooling law
DOI:
https://doi.org/10.33064/iycuaa2014613650Keywords:
fractional calculus, Newton cooling law, Mittag-Leffler functions, fractional differential equations, Caputo derivative, anomalous diffusionAbstract
In this contribution we propose a new fractional differential equation to describe the Newton cooling law. The order of the derivatives is 0<γ ≤1. In order to be consistent with the physical equation, a new parameter σ is introduced. This parameter
characterizes the existence of fractional structures in the system. A relation between the fractional order time derivative γ and the new parameter σ is found. Due to this relation, the solutions of the corresponding fractional differential equations are given in terms of the Mittag-Leffler function depending only on the parameter γ. The classical cases are recovered by taking the limit when γ =1.
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De páginas electrónicas
• GUTIÉRREZ, R. E., ROSÁRIO, J. M., y TENREIRO MACHADO, J. T. Fractional Order Calculus: Basic Concepts and Engineering Aplications. Mathematical Problems in Engineering, 2010 Article ID. 375858, 19 pages. Hindawi Publishing Corporation. doi: 10.1155/2010/375858.
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