Fractional Calculus: Models and Numerical Methods

By Dumitru Băleanu, Kai Diethelm, Enrico Scalas, Juan Trujillo. 2012

1,941 citations recorded by the source corpus.

Subfields: Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/165c3edfa4c2a46ec18c647adcad6b70ba136a59

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Citations in the corpus

Theoretical prospects of fractional order weakly singular Volterra Integro differential equations and their approximations with convergence analysis (2021, methodology): “2 Applying J on both sides of (7), and using (3) and (4), we obtain”
Boundary Value Problems for a Class of Sequential Integrodifferential Equations of Fractional Order (2013, background): “The interest in the subject has beenmainly due to the extensive applications of fractional calculus in the mathematicalmodeling of several real-world phenomena occurring in physical and technical sciences; see, for example, [1–4].”
Numerical solution for a class of fractional convection–diffusion equations using the flatlet oblique multiwavelets (2014, background): “We refer the interested reader to Baleanu et al. (2012), Baleanu and Trujillo (2008), Lotfi et al. (2011), Magin et al. (2009), Kayedi et al. (2012), Saadatmandi and Dehghan (2010, 2011a), Saadatmandi et al. (2012),Dehghan et al. (2010a, 2010b), Saadatmandi and Dehghan (2011b), Wang (2006), Wu…”
Positive solutions for a system of nonlocal fractional boundary value problems (2013, background): “Introduction Fractional differential equations describe many phenomena in various fields of engineering and scientific disciplines such as physics, biophysics, chemistry, biology (such as blood flow phenomena), economics, control theory, signal and image processing, aerodynamics, viscoelasticity, el”
On Hadamard fractional integro-differential boundary value problems (2015, background): “For the recent development of the topic, we refer the reader to a series of books and papers [1–13].”
Sobolev Type Fractional Dynamic Equations and Optimal Multi-Integral Controls with Fractional Nonlocal Conditions (2014, methodology): “The reader interested in the development of the theory, methods, and applications of fractional calculus is referred to the books [2, 11, 16, 18, 22, 23, 31, 32, 34] and to the papers [1, 17, 21, 24, 28, 33, 35, 40].”