Theory and Applications of Fractional Differential Equations

By Anatoly A. Kilbas, Hari M. Srivastava, Juan Trujillo. 2006

14,646 citations recorded by the source corpus.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

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Citations in the corpus

fPINNs: Fractional Physics-Informed Neural Networks (2018, background): “The left-hand side of the above equation is a time-fractional derivative of order \gamma , which is defined in the Caputo sense [17]:”
Fractional differential inclusions with fractional separated boundary conditions (2012, background): “It is well known [31] that the solution of fractional differential equation in (2.”
Some Existence and Stability Results for Hilfer-fractional Implicit Differential Equations with Nonlocal Conditions (2018, positive): “(see [19]) The left-sided Riemann–Liouville fractional integral of order α ∈ R of function f(t) is defined by (I 0+f)(t) = 1 Γ(α) ∫ t”
Efficient generalized Laguerre-spectral methods for solving multi-term fractional differential equations on the half line (2014, methodology): “Therefore, the fractional calculus which means the calculus of derivatives and integral of any order started to be used as a powerful tool in various disciplines from science and engineering (Miller and Ross, 1993; Samko et al., 1993; Podlubny, 1999; Kilbas et al., 2006; Magin, 2006; Das, 2008; Laks”
New estimates considering the generalized proportional Hadamard fractional integral operators (2020, background): “The basic information is given in the monograph [37].”
The extended Mittag-Leffler function via fractional calculus (2017, methodology): “In the same paper, they have used the Riemann-Liouville right-sided fractional integral, derivative and generalized Riemann-Liouville derivative operators (see [23, 36]).”
A backward problem for the time‐fractional diffusion equation (2017, background): “The reader may consult [2,8,9] for more about the theory, applications, and history of fractional calculus.”
Exact solutions of nonlinear time fractional partial differential equations by sub‐equation method (2015, background): “Recently, the fractional differential equations (FDEs) play an important role in applied mathematics, physics, chemistry, engineering, biology, fluid flow, signal processing, control theory, systems identification, and fractional dynamics [1–4].”
Dissipativity and Stability Analysis for Fractional Functional Differential Equations (2015, background): “By the asymptotic expansion for the Mittag-Leffler function [27, 17]”
Existence and uniqueness of the solution to uncertain fractional differential equation (2015, background): “Some references about fractional differential equationsmay be seen in [1-8].”