论文标题
有关函数的线性变量分数微分方程的显式解决方案
Explicit solutions for linear variable-coefficient fractional differential equations with respect to functions
论文作者
论文摘要
建立了相对于功能和连续可变系数的复杂分数阶的微分方程的明确解。解决方案的表示是根据某些收敛的无限无限量差异差异算子来给出的，可以广泛有效地用于分析和计算目的。在恒定系数的情况下，该解决方案可以用多变量Mittag-Leffler函数表示。特别是，获得的结果将luchko-gorenflo表示公式扩展到具有可变系数的一般线性分数微分方程，到相对于给定函数的复杂分数衍生物，并将其相对于给定功能。
Explicit solutions of differential equations of complex fractional orders with respect to functions and with continuous variable coefficients are established. The representations of solutions are given in terms of some convergent infinite series of fractional integro-differential operators, which can be widely and efficiently used for analytic and computational purposes. In the case of constant coefficients, the solution can be expressed in terms of the multivariate Mittag-Leffler functions. In particular, the obtained result extends the Luchko-Gorenflo representation formula to a general class of linear fractional differential equations with variable coefficients, to complex fractional derivatives, and to fractional derivatives with respect to a given function.
