分数微分算子和梅林函数

English | PDF | 2022 | 260 Pages | ISBN : N/A | 2.7 MB

Among the numerous applications of the theory of fractional calculus in almost all applied sciences, applications in numerical analysis and various fields of physics and engineering stand out. Applications of inequalities involving function integrals and their derivatives, as well as applications of fractional differentiation inequalities, have motivated many researchers to investigate extensions and generalizations using various fractional differential and integral operators. Of particular importance is the Mittag–Leffler function which, with its generalizations, appears as a solution to differential or integral equations of fractional order. This produced new results for more generalized fractional integral operators containing the Mittag–Leffler function in their kernels.

在几乎所有的应用科学领域中，分数微积分理论的应用众多，数值分析和各种物理与工程领域的应用尤为突出。涉及函数积分及其导数的不等式应用以及分数微分不等式的应用，激励了许多研究者使用各种分数微分和积分算子来探究这些不等式的扩展和推广。特别重要的是梅特卡夫-勒夫勒（Mittag-Leffler）函数，它作为分数阶方程的解时，出现在其核中。这产生了包含梅特卡夫-勒夫勒函数的新的一般化分数积分算子的结果。

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