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RISA New Method for Laplace Transforms of Multiterm Fractional Differential Equations of the Caputo Type
Publisher: The American Society of Mechanical Engineers (ASME)
Abstract: The Laplace transform method is one of the powerful tools in studying the fractional differential equations (FDEs). In this paper, it is shown that the Heaviside expansion method for integer order differential equations ...
Erratum: “Free Oscillation Solution for Fractional Differential System” (ASME J. Comput. Nonlinear Dyn., 2019, 14(12), p. 124502; DOI: 10.1115/1.4044922)
Publisher: The American Society of Mechanical Engineers (ASME)
Abstract: The error is in Eq. (20) on page 2. This is a well-known definition of the Mittag-Leffler function.The error should be corrected as follows:Error: In Eq. (20), page 2:where Ea,b(z) is the Mittag-Leffler function defined ...
Mode Analysis on Onset of Turing Instability in Time-Fractional Reaction-Subdiffusion Equations by Two-Dimensional Numerical Simulations
Publisher: The American Society of Mechanical Engineers (ASME)
Abstract: There are two types of time-fractional reaction-subdiffusion equations for two species. One of them generalizes the time derivative of species to fractional order, while in the other type, the diffusion term is differentiated ...
Mode Analysis on Onset of Turing Instability in Time-Fractional Reaction-Subdiffusion Equations by Two-Dimensional Numerical Simulations
Publisher: American Society of Mechanical Engineers (ASME)
Abstract: There are two types of time-fractional reaction-subdiffusion equations for two species. One of them generalizes the time derivative of species to fractional order, while in the other type, the diffusion term is differentiated ...
Fractional Derivative Constitutive Models for Finite Deformation of Viscoelastic Materials
Publisher: The American Society of Mechanical Engineers (ASME)
Abstract: A methodology to derive fractional derivative constitutive models for finite deformation of viscoelastic materials is proposed in a continuum mechanics treatment. Fractional derivative models are generalizations of the ...
A Numerical Method for Caputo Differential Equations and Application of High-Speed Algorithm
Publisher: American Society of Mechanical Engineers (ASME)
Abstract: In this paper, a numerical algorithm to solve Caputo differential equations is proposed. The proposed algorithm utilizes the R2 algorithm for fractional integration based on the fact that the Caputo derivative of a function ...
Three-Dimensional Finite Element Simulations on Impact Responses of Gels With Fractional Derivative Models
Publisher: The American Society of Mechanical Engineers (ASME)
Abstract: Fractional derivative constitutive models, developed by the present authors (CND, vol.10, 061002, 2015), are implemented into a commercial finite element (FE) software, abaqus (referred to as a computational model) for ...
A Fractional-Derivative Interpretation of Viscoelastic Rubbers—Part II: Application to Filled and Vulcanized Rubbers Under Large Compression
Publisher: The American Society of Mechanical Engineers (ASME)
Abstract: Abstract. This paper explains the stress behavior of filled and vulcanized rubbers subject to large deformations by using the fractional derivatives proposed in a paper in this series (Fukunaga et al., 2025, “A Fractional ...