From Newton's Equation to Fractional Diffusion and Wave Equations

[摘要] Fractional calculus represents a natural instrument to model nonlocal (or long-range dependence) phenomena either in space or time. The processes that involve different space and time scales appear in a wide range of contexts, from physics and chemistry to biology and engineering. In many of these problems, the dynamics of the system can be formulated in terms of fractional differential equations which include the nonlocal effects either in space or time. We give a brief, nonexhaustive, panoramic view of the mathematical tools associated with fractional calculus as well as a description of some fields where either it is applied or could be potentially applied.

[学科分类] 数学（综合）

[关键词] Fractal Dimension;Dirac Equation;Fractional Derivative;Fractional Calculus;Fractional Differential Equation