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...

A new method that enables easy and convenient discretization of partial differential equations with derivatives of arbitrary real order (so-called fractional derivatives) and delays is presented and illustrated on numerical solution of various types of fractional diffusion equation. The suggested method is the development of Podlubny’s matrix approach (Fractional Calculus and Applied Analysis, ...

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

The purpose of this presentation is to describe a recent family of basis functions—the fractional B-splines—which appear to be intimately connected to fractional calculus. Among other properties, we show that they are the convolution kernels that link the discrete (finite differences) and continuous (derivatives) fractional differentiation operators. We also provide simple closed forms for the ...

The fractional calculus in the neuronal models provides memory properties. In fractional-order model, dynamics of neuron depends on derivative order, which can produce various types memory-dependent dynamics. this paper, behaviors coupled FitzHugh–Nagumo neurons are investigated. effects coupling strength and order under consideration. It is revealed that level synchronization decreased by decr...

In this paper, we prove the existence of mild solutions for the semilinear fractional order functional of Volterra-Fredholm type differential equations with impulses 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. ifx