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Showing 1 to 6 of 6 for “"fractional integrals"”.
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ON GENERALIZED FRACTIONAL INTEGRALS AND DERIVATIVES
… we present a generalization to two existing fractional integrals and derivatives, namely, the Riemann-Liouville and Hadamard fractional operators. The existence and uniqueness results for single term fractional differential equations (FDE) have also been established. We also obtain the Mellin …
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Nonlinear vibration analysis of viscoelastic plates with fractional damping
Fractional calculus has the history as long as the classical calculus, but up to recent years, less attention has been paid to this method due to its complexity and difficulties in dealing with fractional derivatives and fractional integrals. In the present study, the nonlinear vibration analysis …
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Renormalization analysis of continuum models on fractal domains
… to fractal media which are specified by a fractional mass scaling law of the resolution length scale R. The focus is on pre-fractal media (i.e., those with lower and upper cut-offs) through renormalization analysis into continuum models, in which the fractal dimension D is also the order of …
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Non-Markovian stochastic processes and their applications: from anomalous diffusion to time series analysis
… the study of H-sssi processes, we focused on fractional Brownian motion (fBm) and its discrete-time increment process, the fractional Gaussian noise (fGn), which provide examples of non-Markovian Gaussian processes. The fGn, together with stationary FARIMA processes, is widely used in the …
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Elastodynamics and wave propagation in fractal media
… of waves in this model is first developed from fractional hydrodynamic laws, and then, boundary value problems are solved analytically and numerically on spherical domains. In the second model, the fractality is direction dependent, thus the designation ``anisotropic''. This model, which …
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Analysis in Fractional Calculus and Asymptotics Related to Zeta Functions
… -- and even united -- by means of pure analysis. Fractional calculus is the study of differentiation and integration to non-integer orders. Dating back to Leibniz, this idea was considered by many great mathematical figures, and in recent decades it has been used to model many real-world systems …