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Accelerator and Multiplier for Macroeconomic Processes with Memory

“…where is a weighting function (see Allen, R. G. D. (1959), p. [25][26] that satisfies the normalization (τ) K condition (τ)dτ .…”

Fractional Order Estimation Schemes for Fractional and Integer Order Systems with Constant and Variable Fractional Order Colored Noise

“…The applications of variable order derivatives and integrals can also be found in signal processing [24]. In the literature [16,36], three general types of variable order derivative definitions can be found, however, in this paper, the only one (first) definition of the generalization of fractional order difference for variable in time order will be used.…”

Numerical approximate solutions for variable-order Riesz fractional equations via adaptive method

“…Fractional calculus can model price volatility in finance, in hydrology to model fast spreading of pollutants, the generation of fractional Brownian motion as a representation of aquifer material with long-range correlation structure, the particle motions in a heterogeneous environment and long particle jumps of the anomalous diffusion in physics [1,2,5,7,12,14]. Using the concept of variable-order fractional integration and differentiation [11], some diffusion processes in response to temperature changes may be better described. Generally speaking, there is a little difficult that we gain exact analytic solutions of fractional differential equation, and so the approximate and numerical techniques can be introduced and used.…”