• Corpus ID: 55058425

Theorem for Series in Three-Parameter Mittag-Leffler Function

@article{Soubhia2010TheoremFS,
  title={Theorem for Series in Three-Parameter Mittag-Leffler Function},
  author={Ana Luisa Soubhia and Rubens de Figueiredo Camargo and E. Capelas De Oliveira and J. Jr. Vaz},
  journal={Fractional Calculus and Applied Analysis},
  year={2010},
  volume={13},
  pages={9-20}
}
The new result presented here is a theorem involving series in the threeparameter Mittag-Le†er function. As a by-product, we recover some known results and discuss corollaries. As an application, we obtain the solution of a fractional difierential equation associated with a RLC electrical circuit in a closed form, in terms of the two-parameter Mittag-Le†er function. 

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References

SHOWING 1-10 OF 22 REFERENCES

On the Generalized Mittag-Leffler Function and its Application in a Fractional Telegraph Equation

The classical Mittag-Leffler functions, involving one- and two-parameter, play an important role in the study of fractional-order differential (and integral) equations. The so-called generalized

Solution of the fractional Langevin equation and the Mittag–Leffler functions

We introduce the fractional generalized Langevin equation in the absence of a deterministic field, with two deterministic conditions for a particle with unitary mass, i.e., an initial condition and

A coherent approach to non-integer order derivatives

A SINGULAR INTEGRAL EQUATION WITH A GENERALIZED MITTAG LEFFLER FUNCTION IN THE KERNEL

is an entire function of order $({\rm Re}\alpha)^{-1}$ and contains several well-known special functions as particular cases. We define a linear operator $\mathfrak{C}(\alpha, \beta;\rho;\lambda)$ on

On some fractional Green’s functions

In this paper we discuss some fractional Green’s functions associated with the fractional differential equations which appear in several fields of science, more precisely, the so-called wave

Applications Of Fractional Calculus In Physics

An introduction to fractional calculus, P.L. Butzer & U. Westphal fractional time evolution, R. Hilfer fractional powers of infinitesimal generators of semigroups, U. Westphal fractional differences,