Abstract
In the paper, we propose an analytical method which is based on combination of the method of steps and the fractional Laplace transform that will be used together to find exact solutions or approximations to homogeneous and non-homogeneous fractional differential equations with constant delays and possible extension to time-dependent delays. The applicability of this technique is demonstrated by several examples. The results show that the approach is correct, accurate and easy to implement for solving delayed fractional differential equations near the origin.
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