Threefold Introduction to Fractional Derivatives

By Rudolf Hilfer. 2008

214 citations recorded by the source corpus.

Subfields: Mathematical Physics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/6a39412b78d01847cebc5e9673e6d0ce14987e4d

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Citations in the corpus

Hyers‐Ulam stability analysis to implicit Cauchy problem of fractional differential equations with impulsive conditions (2018, background): “We see that for any μ ∈ (0, 1), the integer-order system (1) is unstable.”
Heat transfer analysis in a second grade fluid over and oscillating vertical plate using fractional Caputo–Fabrizio derivatives (2016, methodology): “The fractional derivatives used most are the Riemann–Liouville fractional derivative and the Caputo fractional derivative [3,4].”
Fractional and operational calculus with generalized fractional derivative operators and Mittag–Leffler type functions (2010, methodology): “Example 1 If we put g (x) = xμ−1 in Theorem 8 and apply the special case of the following integral formula when γ = 1 [8], then ∫ x”
Fractional Calculus: Quo Vadimus? (Where are we Going?) (2015, background): “For questions, discussions and (partial) answers, see [28]: http://www.”
Generalized Cauchy type problems for nonlinear fractional differential equations with composite fractional derivative operator (2012, background): “Applications of D a+ are given in [7,2,12,13].”
The existence and Ulam–Hyers stability results for $$\psi $$-Hilfer fractional integrodifferential equations (2020, unknown): “2 The operator Dθ1,θ2;ψ a+ is an interpolator of the following fractional derivatives: (i): Standard Hilfer when ψ(t) → t [12], Hilfer–Hadamard when ψ(t) → log t [14], Hilfer–Katugampola for ψ(t) → t, ρ > 0 [19]; (ii): Standard Riemann–Liouville for ψ(t) → t, θ2 → 0 [15], Caputo-type for ψ(t) → t, θ”