HADAMARD-TYPE FRACTIONAL CALCULUS

By Anatoly A. Kilbas. 2001

374 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/527c49bfbfa6f4ff5e1777ad123d87b96958da1c

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Citations in the corpus

New fractional integral unifying six existing fractional integrals (2016, background): “Recent results about the Hadamard and Hadamard-type integrals such as Hadamard-type fractional calculus [21], composition and semigroup properties [7], Mellin transforms [6], integration by parts formulae [8], Gtransform representations [22], impulsive differential equations with Hadamard fractional”
An Existence Theorem for Fractional Hybrid Differential Inclusions of Hadamard Type with Dirichlet Boundary Conditions (2014, background): “A detailed description of Hadamard fractional derivative and integral can be found in [2, 21, 22, 23, 24, 25].”
On Hadamard fractional integro-differential boundary value problems (2015, background): “Details and properties of Hadamard fractional derivative and integral can be found in [2,15–19].”
Weighted Fractional Calculus: A General Class of Operators (2022, background): “If w(x) = x is a power function and φ(x) = log(x) is the natural logarithm function, then the operators of w-weighted fractional calculus with respect to φ become precisely those of Hadamardtype fractional calculus, defined [22, 23] as follows:”
Finite Difference Methods for Caputo–Hadamard Fractional Differential Equations (2020, background): “2) Although Hadamard fractional derivative was proposed early in 1892 [8], there are few studies for this fractional derivative problem except [2,6,7, 10,16,17].”
On some operators involving Hadamard derivatives (2013, methodology): “(2.3) A more general Hadamard-type fractional operator has been studied by Kilbas [7].”
Generalized fractional derivatives and Laplace transform (2020, background): “After then, the corresponding derivatives are defined (see for example [20, 17, 18, 14, 12, 15, 16]).”
Caputo-Hadamard fractional differential equations in banach spaces (2018, background): “and Hadamard fractional derivatives (see [3, 5, 7, 8, 12, 14]), and the references therein.”
Tempered and Hadamard-Type Fractional Calculus with Respect to Functions (2019, background): “See also [4, 21] for these results.”
A NEW APPROACH TO GENERALIZED FRACTIONAL DERIVATIVES (2011, background): “, investigate properties of Hadamard fractional integral and deriva tive [1, 2, 3, 9, 11, 12, 14, 17].”
New Hermite–Jensen–Mercer-type inequalities via k-fractional integrals (2020, background): “It also corresponds the Hadamard fractional integral [63] once we take θ = 0 and α → 0 in the generalized fractional integral.”
Existence and uniqueness of solutions to fractional differential equations in the frame of generalized Caputo fractional derivatives (2018, background): “The Hadamard type fractional integrals and derivatives were introduced in [9].”