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The direct spectral problem via local derivative including truncated Mittag-Leffler function
Applied Mathematics and Computation, 2020In this article, we propose some substantial spectral data for Sturm–Liouville problem with separated boundary conditions in frame of newly defined truncated M-derivative which contains truncated Mittag-Leffler function.
E. Baş, B. Acay
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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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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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Iranian Journal of Science and Technology, Transactions of Mechanical Engineering, 2023
A. Soleiman +3 more
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A. Soleiman +3 more
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Chaos, Solitons & Fractals, 2018
Non-Fickian or anomalous diffusion had been well documented in material transport through heterogeneous systems at all scales, whose dynamics can be quantified by the time fractional derivative equations (fDEs).
Xiangnan Yu +3 more
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Non-Fickian or anomalous diffusion had been well documented in material transport through heterogeneous systems at all scales, whose dynamics can be quantified by the time fractional derivative equations (fDEs).
Xiangnan Yu +3 more
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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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Some properties of bivariate Mittag-Leffler function
The Journal of Analysis, 2023M. Shahwan +2 more
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