Generalized mittag-leffler function and generalized fractional calculus operators

By Anatoly A. Kilbas, M. Saigo, R. K. Saxena. 2004

583 citations recorded by the source corpus.

Subfields: Mechanics of Materials, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/2cfb9a89d0e87e9bcc2c5bf2e39527dbe919b2f2

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In Mechanics of Materials

In Modeling and Simulation

In Numerical Analysis

Citations in the corpus

Why fractional derivatives with nonsingular kernels should not be used (2020, methodology): “Introduced in [3] to provide a Caputo-like regularization of the operator previously introduced in [14], the Prabhakar derivative is defined as”
Some properties of Prabhakar-type fractional calculus operators (2015, background): “The Prabhakar integral is hence defined as follows [24, 17].”
On a Fractional Operator Combining Proportional and Classical Differintegrals (2020, background): “The Prabhakar fractional integral is defined [22,23] by:”
Global Padé Approximations of the Generalized Mittag-Leffler Function and its Inverse (2013, background): “Later on, some studies [5, 4, 12, 17, 13, 22, 10] contributed to several properties and applications of the (generalized) Mittag-Leffler functions.”
Hermite‐Hadamard inequalities in fractional calculus defined using Mittag‐Leffler kernels (2020, methodology): “We replace α by kν in the Hermite-Hadamard inequality for RL integrals (22):”
ON GENERALIZED WRIGHT'S HYPERGEOMETRIC FUNCTIONS AND FRACTIONAL CALCULUS OPERATORS (2005, background): “10) correspond to the results given in [2].”
More properties of the proportional fractional integrals and derivatives of a function with respect to another function (2020, background): “where Eα,β is the Mittag-Leffler function of two parameters [29].”
Fractional calculus with an integral operator containing a generalized Mittag-Leffler function in the kernel (2009, background): “Compositional properties of the integral operator involving the generalized Mittag–Leffler function E a;bðzÞ with different indices In this section, we first present a generalization of the following known identity (see, for details, [12,20]): Z x”
A practical guide to Prabhakar fractional calculus (2020, background): “For the sake of completeness, one also has that (see [80]) J t0J γ α,β,λ;t0 f(t) = J γα,β+σ,λ;t0f(t) = J γ α,β,λ;t0 [ J t0f(t) ] , for f ∈ L1[t0, T ] and σ > 0.”
Lamperti-type laws (2007, background): “2007/02/20 file: ArLamperti.tex date: August 31, 2009 Mittag-Leffler type functions which are discussed, for, instance in Kilbas, Saigo and Megumi (55).”
Integration by parts and its applications of a new nonlocal fractional derivative with Mittag-Leffler nonsingular kernel (2016, unknown): “From [10] we recall the relation between the Riemann-Liouville and Caputo new derivatives as ( ABC 0D f)(t) = ( ABR 0D f)(t) − B(α) 1− α f(0)Eα(− α 1− α t) (16) From [13] recall the (left) generalized fractional integral operator ( E ρ,μ,ω,a+ φ)(x) = ∫ x”