Abstract The research of a formulation to model non-local interactions in the mechanical behavior matter is currently an open problem. In this context, strong based on fractional calculus provided paper. This derived from analogy with long-memory viscoelastic models. Specifically, same kind power-law time-dependent kernel used Boltzmann integral stress-strain relation as Fredholm relation. lead...

Firstly the one-dimension digital fractional order SavitzkyGolay differentiator (1-D DFOSGD), which generalizes the Savitzky-Golay filter from the integer order to the fractional order, is proposed to estimate the fractional order derivative of the noisy signal. The polynomial least square fitting technology and the Riemann-Liouville fractional order derivative definition are used to ensure rob...

In order to solve the local fractional differential equations, we couple residual method with Adomian decomposition via calculus operator. Several examples are given illustrate solution process and reliability of method.

Inventory control is considered one of the most widely documented topics in reality. Fractional derivatives and integration part fractional calculus. calculus generalized ordinary The memory physical phenomena a highly concerning topic but it neglected with describing terms integer-order differential equation. To discuss inventory model, derivative tools are considered. A at any point gives pre...

This paper analyses the dynamical properties of systems with backlash and impact phenomena based on the describing function method. It is shown that this type of nonlinearity can be analyzed in the perspective of the fractional calculus theory. The fractional-order dynamics is illustrated using the Nyquist plot and the results are compared with those of standard models.

In this paper, we prove the existence of mild solutions for the semilinear fractional order functional of VolterraFredholm type differential equations with nonlocal conditions in a Banach space. The results are obtained by using the theory of fractional calculus, the analytic semigroup theory of linear operators and the fixed point techniques. MSC: 34K37 • 34A08 • 47H10