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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
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2015
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tom 13
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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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The Umbral operator and the integration involving generalized Bessel-type functions

81%
Nisar K. S., Mondal S. R., Agarwal P., Al-Dhaifallah M.
Open Mathematics
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2015
|
tom 13
|
nr 1
EN
The main purpose of this paper is to introduce a class of new integrals involving generalized Bessel functions and generalized Struve functions by using operational method and umbral formalization of Ramanujan master theorem. Their connections with trigonometric functions with several distinct complex arguments are also presented.
3
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The general solution for impulsive differential equations with Riemann-Liouville fractional-order q ∈ (1,2)

81%
Zhang X., Agarwal P., Liu Z., Peng H.
Open Mathematics
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2015
|
tom 13
|
nr 1
EN
In this paper we consider the generalized impulsive system with Riemann-Liouville fractional-order q ∈ (1,2) and obtained the error of the approximate solution for this impulsive system by analyzing of the limit case (as impulses approach zero), as well as find the formula for a general solution. Furthermore, an example is given to illustrate the importance of our results.
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