Fractional calculus with an integral operator containing a generalized Mittag-Leffler function in the kernel

By Hari M. Srivastava, Ivorad Tomovski. Applied Mathematics and Computation, 2009

521 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mechanics of Materials, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/3cdd280638dbb06f0e9a776c7eb5731d73b4db20

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Mechanics of Materials

In Modeling and Simulation

Citations in the corpus

Operational method for solving multi-term fractional differential equations with the generalized fractional derivatives (2013, background): “Some properties and applications of the GRLFD are given in [3, 4, 18, 20, 21, 22].”
Advanced Local Fractional Calculus and Its Applications (2012, unknown): “[148] H.”
A Mittag-Leffler-type function of two variables (2013, methodology): “[9] Srivastava HM, Tomovski Z. Fractional calculus with an integral operator containing a generalized Mittag-Leffler function in the kernel.”
Integral inequalities for a fractional operator of a function with respect to another function with nonsingular kernel (2020, background): “5 can be seen as a special case of the generalized Prabhakar model defined in [57].”
On Ostrowski type inequalities (2016, background): “By choosing parameters suitably in (51) and (52), many important fractional integral operators including those involving the generalized Mittag-Leffler function as kernel (see [15], [16] and [18]) can be easily obtained and corresponding to these integral operators related inequalities from the Coro”
Integral and computational representations of the extended Hurwitz–Lerch zeta function (2011, background): “respectively (see also several general families of Mittag–Leffler type functions which were investigated and applied recently by Srivastava and Tomovski [31]).”
On the ψ-Hilfer fractional derivative (2017, background): “[2, 22] The Hilfer fractional derivatives (left-sided and right-sided) D a+ of function f ∈ C(a, b) of order n− 1 < α < n and type 0 ≤ β ≤ 1, are defined by D a+ f (x) = I γ−α a+ (”
A study of fractional integral operators involving a certain generalized multi‐index Mittag‐Leffler function (2018, background): “where (and throughout our presentation) (λ)ν denotes the general Pochhammer symbol or the shifted factorial, since (1)n = n! (n ∈ N0 ∶= N ∪ {0}; N ∶= {1, 2, 3, · · ·}), defined (for λ, ν ∈ C and in terms of the familiar Gamma function) by (λ)ν ∶= Γ(λ + ν) Γ(λ) = { 1 (ν = 0; λ ∈ C∖{0}) λ(λ + 1)· · ·(”
Some New Fractional-Calculus Connections between Mittag–Leffler Functions (2019, methodology): “The above function with a single parameter α has also been extended to more general functions defined with two or more parameters, such as the following [15,16].”
Fractional and operational calculus with generalized fractional derivative operators and Mittag–Leffler type functions (2010, background): “Theorem 1 [24] The following relationship holds true: ( D α,β a+ [ (t − a)ν−1 E μ,ν [ ω (t − a)μ]]) (x) = (x − a)ν−α−1 E μ,ν−α [ω (x − a)μ] (2.”
The extended Mittag-Leffler function via fractional calculus (2017, background): “These results are the extended form of Mittag-Leffler function defined in ([39, 45]).”
Fractional-Order Derivatives and Integrals: Introductory Overview and Recent Developments (2020, background): “Srivastava and Tomovski [96] introduced the following generalization of the Mittag-Leffler function: (4.9) Eγ,κα,β (z) = ∞∑ n=0 (γ)κn Γ (αn+ β) zn n”
The Role of the Mittag-Leffler Function in Fractional Modeling (2015, background): “The most extended source for such information is the recent monograph [1] (see also the papers tightly related to the topic of the monograph [19–22]).”