In this work, we study variational problems with time delay and higher-order distributed-order fractional derivatives dealing a new operator. This derivative combines two known operators: respect to another function. The main results of paper are necessary sufficient optimality conditions for different types problems. Since generalized derivatives, from some well-known can be obtained as partic...

Generalized constitutive relationships of viscoelastic foams are investigated in which the time derivatives of integer order are replaced by derivatives of fractional order. To this point, the justification of such models has resided in the fact that they are effective in describing the behavior of real materials. In this work, the three-parameter fractional Kelvin Voigt model is compared to th...

This study is devoted to constructing an approximate analytic solution of the fractional form a strongly nonlinear boundary value problem with multi-fractional derivatives that comes in chemical reactor theory. We construct algorithm based on generalized differential transform technique four simple steps. The derivative defined sense Caputo. also mathematically prove convergence algorithm. appl...

We give uniform and Lp Caputo-Bochner abstract sequential generalized right fractional Landau inequalities over $\mathbb{R}_{-}$. These estimates the size of second third derivatives a Banach space valued function an application when basic order is 1

In this paper, a method for the digital simulation of wind velocity fields by Fractional Spectral Moment function is proposed. It is shown that by constructing a digital filter whose coefficients are the fractional spectral moments, it is possible to simulate samples of the target process as superposition of Riesz fractional derivatives of a Gaussian white noise processes. The key of this simul...

In this letter we develop a new generalization of the two-dimensional differential transform method that will extend the application of the method to linear partial differential equations with spaceand time-fractional derivatives. The new generalization is based on the two-dimensional differential transform method, generalized Taylor’s formula and Caputo fractional derivative. Several illustrat...

Abstract This article considers a fractional-order neuron model under an electromagnetic field in terms of generalized Caputo fractional derivatives. The motivation for incorporating derivatives the previously proposed integer-order is that impresses with efficient effects memory, and parameters orders can increase performance by amplifying degree freedom. results on uniqueness solution are est...

In this work we study variational problems, where ordinary derivatives are replaced by a generalized proportional fractional derivative. This operator depends on fixed parameter, acting as weight over the state function and its first-order We consider problem with without boundary conditions, additional restrictions like isoperimetric holonomic. Herglotz’s when in presence of time delays also c...