The notion of the Riemann-Liouville fractional integral is introduced as a natural generalization of the repeated integral written in a convolution type form. The Riemann-Liouville fractional derivative is defined as left-inverse to the Riemann-Liouville fractional integral. The Caputo fractional ...
besides the classical approach based on a combination in series or parallel of standard mechanical elements as springs and dashpots, particular emphasis is given to the application of models whose constitutive equations are based on differential equations of fractional order (Fractional Derivative Model)...
Nonlinear fractional differential equations (NLFDEs) are broadly used to give an explanation for various phenomena in specific fields of science and engineering. Applications of NLFDEs may be found in turbulence, fluid dynamics, and nonlinear biological systems. NLFDEs are believed to be powerful tool...
Various orders of FDs are analyzed and the numerical results converge toward the analytical solutions as the order of derivative goes toward the integer value of 1, and therefore verifies the numerical scheme. Parameter studies of problems with different initial conditions indicate that the method ...
This paper presents a semi-analytical solution to one-dimensional consolidation equation of fractional derivative Kelvin-Voigt viscoelastic saturated soils subjected to different time-dependent loadings. The theory of fractional calculus is first introduced to Kelvin-Voigt constitutive model to describe consoli...
Fractional-order calculus has been successfully used in solid mechanics, material mechanics, biomechanics, control system dynamics, fractal media, thermodynamics, as well as in several others emerging fields of physical and engineering sciences. Besides these promising applications little work has still be...
Bachher, M., Sarkarx, N., Lahiri, A.: Generalized thermoelastic infinite medium with voids subjected to a instantaneous heat sources with fractional derivative heat transfer. Int. J. Mech. Sci. 89, 84–91 (2014) Article MATH Google Scholar Alzahrani, F.S., Abbas, I.A.: Fractional or...
Expressions for creep and relaxation functions, in terms of the Mittag-Leffler function that depends on the fractional derivative parameter β, are obtained. These creep and relaxation functions allow for significant creep or relaxation to occur over many decade intervals when the memory parameter, β...
The fractional derivative has been occurring in many physical problems, such as frequency-dependent damping behavior of materials, motion of a large thin p... SS Ray,BP Poddar,RK Bera - 《Journal of Applied Mechanics》 被引量: 113发表: 2005年 LORD-SHULMAN THEORY UNDER THE DEPENDENCE OF THE...
the Caputo derivative is replaced with a quadrature formula, then an implicit method is used for the remaining part. In the linear case, the proposed strategy reduces the time fractional models into linear simultaneous equations. In nonlinear cases, Quasilinearization is utilized to tackle the nonlin...