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Certain Integrals Involving Generalized Mittag-Leffler Functions
Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Agarwal, P., Chand, M., Jain, Shilpi
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Mittag-Leffler and Wright Functions
2021The exponential function \(e^z\) plays an extremely important role in the theory of integer-order differential equations. For fdes, its role is subsumed by the Mittag-Leffler and Wright functions. In this chapter, we discuss their basic analytic properties and numerical computation.
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2019
In the previous chapter, we presented the classic hypergeometric functions that constitute the functions associated with the integer order calculus, in particular, a generalization of the factorial concept by the gamma function. In a similar way, we can understand why fractional calculus is an important tool for refining the description of many natural
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In the previous chapter, we presented the classic hypergeometric functions that constitute the functions associated with the integer order calculus, in particular, a generalization of the factorial concept by the gamma function. In a similar way, we can understand why fractional calculus is an important tool for refining the description of many natural
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The Classical Mittag-Leffler Function
2014In this chapter we present the basic properties of the classical Mittag-Leffler function E α (z) (see (1.0.1)). The material can be formally divided into two parts.
Rudolf Gorenflo +3 more
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2010
This chapter is devoted to a brief summary of the most important properties of Mittag-Leffler functions. These functions play a fundamental role in many questions related to fractional differential equations, and they will be used frequently in the later chapters.
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This chapter is devoted to a brief summary of the most important properties of Mittag-Leffler functions. These functions play a fundamental role in many questions related to fractional differential equations, and they will be used frequently in the later chapters.
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Multi-index Mittag-Leffler Functions
2014Consider the function defined for \(\alpha _{1},\ \alpha _{2} \in \mathbb{R}\) (α 1 2 +α 2 2 ≠ 0) and \(\beta _{1},\beta _{2} \in \mathbb{C}\) by the series $$\displaystyle{ E_{\alpha _{1},\beta _{1};\alpha _{2},\beta _{2}}(z) \equiv \sum _{k=0}^{\infty } \frac{z^{k}} {\varGamma (\alpha _{1}k +\beta _{1})\varGamma (\alpha _{2}k +\beta _{2})}\ \ (z \
Rudolf Gorenflo +3 more
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When is a Mittag–Leffler function a Nussbaum function?
Automatica, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Li, Yan, Chen, Yangquan
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Mittag-Leffler type functions of three variables
Mathematical Methods in the Applied SciencesIn this article, we generalized Mittag-Leffler-type functions F~̵̄ A ( 3 ) , F~̵̄ B ( 3 ) , F~̵̄ C ( 3 ) and F~̵̄ D ( 3 ) , which correspond, respectively, to the familiar Lauricella hypergeometric functions F A ( 3 ) , F B ( 3 ) , F C ( 3 ) and F D ( 3 ) of three variables.
Anvar Hasanov, Hilola Yuldashova
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Generalized Fourier Multipliers via Mittag-Leffler Functions
Mediterranean Journal of MathematicsFourier multipliers have played an important role in harmonic analysis since from the outset. They play a decisive role in studying several integral operators such as singular integral operators, oscillatory integral operators, maximal functions, and Littlewood-Paley \(g\)-functions, among others.
Hawawsheh, Laith, Al-Salman, Ahmad
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Estimates for Integrals with Mittag-Leffler Functions
Lobachevskii Journal of MathematicszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ikromov, Isroil A., Safarov, Akbar R.
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