Comprehensive Inequalities and Equations Specified by the Mittag-Leffler Functions and Fractional Calculus in the Complex Plane

2018 ◽  
pp. 295-310
Author(s):  
Hüseyin Irmak ◽  
Praveen Agarwal
Keyword(s):  
Fractional Calculus ◽  
Complex Plane

scholarly journals Modified Mittag-Leffler Functions with Applications in Complex Formulae for Fractional Calculus

2020 ◽  
Vol 4 (3) ◽  
pp. 45
Author(s):  
Arran Fernandez ◽  
Iftikhar Husain
Keyword(s):  
Differential Equations ◽  
Fractional Calculus ◽  
Complex Plane ◽  
Fractional Differential Equations ◽  
Complex Analysis ◽  
Fractional Calculus Operators ◽  
Fractional Differential

Mittag-Leffler functions and their variations are a popular topic of study at the present time, mostly due to their applications in fractional calculus and fractional differential equations. Here we propose a modification of the usual Mittag-Leffler functions of one, two, or three parameters, which is ideally suited for extending certain fractional-calculus operators into the complex plane. Complex analysis has been underused in combination with fractional calculus, especially with newly developed operators like those with Mittag-Leffler kernels. Here we show the natural analytic continuations of these operators using the modified Mittag-Leffler functions defined in this paper.

Fractional Calculus in Bioengineering, Part 1

2004 ◽  
Vol 32 (1) ◽  
pp. 1-104 ◽  
Author(s):  
Richard L. Magin
Keyword(s):  
Fractional Calculus

THE STATE OF THE ART OF THE THEODORSEN'S AEROELASTIC THEORY BY A FRACTIONAL CALCULUS APPROACH

2019 ◽  
Author(s):  
Cassiano Arruda ◽  
André Cunha Filho ◽  
Antonio Marcos de Lima
Keyword(s):  
Fractional Calculus ◽  
State Of The Art ◽  
The State

Rough integration via fractional calculus

2020 ◽  
Vol 72 (1) ◽  
pp. 39-62 ◽  
Author(s):  
Yu Ito
Keyword(s):  
Fractional Calculus

A system of functions biorthogonal with the derivatives of Chebyshev second-kind polynomials of a complex variable

2020 ◽  
Vol 17 (2) ◽  
pp. 256-277
Author(s):  
Ol'ga Veselovska ◽  
Veronika Dostoina
Keyword(s):  
Complex Plane ◽  
Complex Variable ◽  
Analytic Functions ◽  
Combinatorial Identities ◽  
Independent Interest ◽  
Closed Curves ◽  
In Series ◽  
Derivatives Of

For the derivatives of Chebyshev second-kind polynomials of a complex vafiable, a system of functions biorthogonal with them on closed curves of the complex plane is constructed. Properties of these functions and the conditions of expansion of analytic functions in series in polynomials under consideration are established. The examples of such expansions are given. In addition, we obtain some combinatorial identities of independent interest.

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