Margarita Rivero

TL;DR: A survey of useful, established formulas in fractional calculus can be found in this paper, where the authors present a survey of the most useful formulas in Fractional Calculus, systematically collected for reference purposes.

TL;DR: The main objective of this paper is to demonstrate the possibility of using fractional differential equations to simulate the dynamics of anomalous processes whose analytical representations are continuous but strongly not differentiable, like Weierstrass-type functions.

TL;DR: It is shown how a generalized matrix exponential function and certain fractional Green function, in connection with the Mittag–Leffler type functions, would allow us to obtain an explicit representation of the general solution to the system (1) when A is a constant matrix.

TL;DR: This paper is an attempt to overcome the situation by reviewing the state of the art of fractional calculus and putting this topic in a systematic form, and several possible routes of future progress that emerge are tackled.

TL;DR: In this article, a generalized Taylor's formula of the kindfx=∑j=0najx−a(j+1)α−1+Tnx, whereaj ∈ R,x > a, 0 ≤ α ≤ 1, is established.