实直线分形子集上的新导数
New Derivatives on Fractal Subset of Real-line
摘要：
本文介绍了定义在分形集上的函数的广义分式Riemann-Liouville和Caputo类导数。在分形集上定义了Gamma、Mittag-Leffler和β函数。给出了非局部拉普拉斯变换，并将其应用于求解线性和非线性分形方程。利用这些新的非局部导数的优点在于，它们被用于更好地模拟过程的记忆效应。
英文摘要：
In this manuscript we introduced the generalized fractional Riemann-Liouville and Caputo like derivative for functions defined on fractal sets. The Gamma, Mittag-Leffler and Beta functions were defined on the fractal sets. The non-local Laplace transformation is given and applied for solving linear and non-linear fractal equations. The advantage of using these new nonlocal derivatives on fractals subset of real-line lies in the fact that they are used for better modelling of processes with memory effect.
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