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Some fractional integral formulas for the Mittag-Leffler type function with four parameters

100%
Agarwal P., Nieto J. J.
Open Mathematics
|
2015
|
tom 13
|
nr 1
EN
In this paper we present some results from the theory of fractional integration operators (of Marichev- Saigo-Maeda type) involving the Mittag-Leffler type function with four parameters ζ , γ, Eμ, ν[z] which has been recently introduced by Garg et al. Some interesting special cases are given to fractional integration operators involving some Special functions.
2
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Existence theory for sequential fractional differential equations with anti-periodic type boundary conditions

81%
Aqlan M. H., Alsaedi A., Ahmad B., Nieto J. J.
Open Mathematics
|
2016
|
tom 14
|
nr 1
723-735
EN
We develop the existence theory for sequential fractional differential equations involving Liouville-Caputo fractional derivative equipped with anti-periodic type (non-separated) and nonlocal integral boundary conditions. Several existence criteria depending on the nonlinearity involved in the problems are presented by means of a variety of tools of the fixed point theory. The applicability of the results is shown with the aid of examples. Our results are not only new in the given configuration but also yield some new special cases for specific choices of parameters involved in the problems.
3
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Extended Riemann-Liouville type fractional derivative operator with applications

81%
Agarwal P., Nieto J. J., Luo M.-J.
Open Mathematics
|
2017
|
tom 15
|
nr 1
1667-1681
EN
The main purpose of this paper is to introduce a class of new extended forms of the beta function, Gauss hypergeometric function and Appell-Lauricella hypergeometric functions by means of the modified Bessel function of the third kind. Some typical generating relations for these extended hypergeometric functions are obtained by defining the extension of the Riemann-Liouville fractional derivative operator. Their connections with elementary functions and Fox’s H-function are also presented.
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