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Geometry, Integrability and Quantization, 2021
Star product for functions of one variable is given. A deformation of the Mittag-Leffler functions is suggested by means of the star product.
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Star product for functions of one variable is given. A deformation of the Mittag-Leffler functions is suggested by means of the star product.
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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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On Zeros of Functions of Mittag--Leffler Type
Mathematical Notes, 2000zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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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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2012
The classical Mittag–Leffler function plays an important role in fractional differential equations. In this chapter we mention in brief the q-analogues of the Mittag–Leffler functions defined by mathematicians. We pay attention to a pair of q-analogues of the Mittag–Leffler function that may be considered as a generalization of the q-exponential ...
Mahmoud H. Annaby, Zeinab S. Mansour
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The classical Mittag–Leffler function plays an important role in fractional differential equations. In this chapter we mention in brief the q-analogues of the Mittag–Leffler functions defined by mathematicians. We pay attention to a pair of q-analogues of the Mittag–Leffler function that may be considered as a generalization of the q-exponential ...
Mahmoud H. Annaby, Zeinab S. Mansour
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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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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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The Mittag-leffler and related functions
Integral Transforms and Special Functions, 1993In our attempts to find solutions of fractional differential equations we are led, in a natural fashion, to the study of certain transcendental functions. These functions may be defined by a fractional integral or combinations of such integrals. Further investigations show that these new functions are intimately related to the classical Mittag-Leffler ...
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