On the fractional calculus of multivariate Mittag-Leffler functions
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DOI: 10.1080/00207160.2021.1906869
Abstract: ABSTRACT Multivariate Mittag-Leffler functions are a strong generalisation of the univariate and bivariate Mittag-Leffler functions which are known to be important in fractional calculus. We consider the general functional operator defined by an integral transform… read more here.
Keywords: mittag leffler; leffler functions; fractional calculus; multivariate mittag ... See more keywords
Mittag–Leffler functions, lp n-balls and geometric pairings
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DOI: 10.1080/10652469.2016.1267730
Abstract: ABSTRACTWe deal with the relation between the Mittag–Leffler functions and the sum of the hypervolume of generalized lp n-balls. We derive from this result some simple properties of the Mittag–Leffler functions. We also define some… read more here.
Keywords: balls geometric; geometric pairings; mittag leffler; functions balls ... See more keywords
Mixed Fractional Differential Equations and Generalized Operator-Valued Mittag-Leffler Functions
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DOI: 10.1134/s0001434619110087
Abstract: We introduce the most general mixed fractional derivatives and integrals from three points of views: probability, the theory of operator semigroups, and the theory of generalized functions. The solutions to the resulting mixed fractional PDEs… read more here.
Keywords: mixed fractional; mittag leffler; fractional differential; leffler functions ... See more keywords
Hadamard and Fejér–Hadamard Inequalities for Further Generalized Fractional Integrals Involving Mittag-Leffler Functions
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DOI: 10.1155/2021/5589405
Abstract: In this paper, generalized versions of Hadamard and Fejer–Hadamard type fractional integral inequalities are obtained. By using generalized fractional integrals containing Mittag-Leffler functions, some well-known results for convex and harmonically convex functions are generalized. The… read more here.
Keywords: fractional integrals; generalized fractional; hadamard; mittag leffler ... See more keywords
The composition of extended Mittag-Leffler functions with pathway integral operator
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DOI: 10.1186/s13662-017-1237-8
Abstract: In this paper, we present certain composition formulae of the pathway fractional integral operators associated with two extended Mittag-Leffler functions. Here, we find out the relevant connections of some particular cases of the main results… read more here.
Keywords: leffler functions; composition extended; mittag leffler; extended mittag ... See more keywords
The numerical algorithms for discrete Mittag-Leffler functions approximation
Sign Up to like & getrecommendations! Published in 2019 at "Fractional Calculus and Applied Analysis"
DOI: 10.1515/fca-2019-0006
Abstract: Abstract Motivated essentially by the success of the applications of the discrete Mittag-Leffler functions (DMLF) in many areas of science and engineering, the authors present, in a unified manner, a detailed numerical implementation method of… read more here.
Keywords: leffler functions; discrete mittag; mittag leffler; numerical algorithms ... See more keywords
Certain New Class of Analytic Functions Defined by Using a Fractional Derivative and Mittag-Leffler Functions
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DOI: 10.3390/axioms11110655
Abstract: Fractional calculus has a number of applications in the field of science, specially in mathematics. In this paper, we discuss some applications of fractional differential operators in the field of geometric function theory. Here, we… read more here.
Keywords: leffler functions; analytic functions; mittag leffler; new class ... See more keywords
Some New Fractional-Calculus Connections between Mittag–Leffler Functions
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DOI: 10.3390/math7060485
Abstract: We consider the well-known Mittag–Leffler functions of one, two and three parameters, and establish some new connections between them using fractional calculus. In particular, we express the three-parameter Mittag–Leffler function as a fractional derivative of… read more here.
Keywords: fractional calculus; leffler functions; parameter; mittag leffler ... See more keywords
Applications of a q-Differential Operator to a Class of Harmonic Mappings Defined by q-Mittag-Leffler Functions
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DOI: 10.3390/sym14091905
Abstract: Many diverse subclasses of analytic functions, q-starlike functions, and symmetric q-starlike functions have been studied and analyzed by using q-analogous values of integral and derivative operators. In this paper, we define a q-analogous value of… read more here.
Keywords: leffler functions; operator; class; mittag leffler ... See more keywords