of Hamilton's type are given. Hamilton's action integral in the first principle, do not coincide with the lower bound in the fractional integral, while in the second principle the minimization is performed with respect to a function from a specified space and the order of fractional derivative...
The Caputo-Fabrizio fractional derivative is analyzed in classical and distributional settings. The integral inequalities needed for application in linear viscoelasticity are presented. They are obtained from the entropy inequality in a weak form. Moreover, integration by parts, an expansion formula, appr...
A fractional derivative with non-singular kernel for interval-valued functions under uncertainty The purpose of the current investigation is to generalize the concept of fractional derivative in the sense of Caputo-Fabrizio derivative (CF-derivative) f... S Salahshour,A Ahmadian,F Ismail,... - Op...
I. Maritchev, Integrals and Derivatives of the Fractional Order and Some of Their Applications, in Russian, Nauka i Tekhnika, Minsk, Belarus, 1987. Search in Google Scholar [5] M. Caputo, “Linear models of dissipation whose Q is almost frequency independent, part II,” Geophysical Journal ...
In some sense this can be thought of as a discrete form of the ordinary derivative of a function. In particular, (1.1) computes the amount of change infas we move the time point fromtto. An important feature of the forward difference operator is its local structure. By this we mean that...
This paper formulates explicit necessary and sufficient conditions for the local asymptotic stability of equilibrium points of the fractional differential equation $$\begin{aligned} {D}^{\alpha }y(t)+f(y(t),\, {D}^{\beta }y(t))=0,\quad t>0 \end{aligned}$$ involving two Caputo deri...
Study of new class of q-fractional derivative and its properties There are several approaches to the fractional differential operator. Generalized q-fractional difference operator was defined in the aid of q-iterated Cauchy integral and q-calculus techniques. We introduce Caputo type derivative relate....
is the left caputo fractional derivative of order \(\alpha \in (0,1)\) (see definition 3 ). in recent years, the study of differential equations using non-local fractional operators has attracted a lot of interest. the time-space fractional diffusion equations could be applied to a wide ...
Spectral approximations to the fractional integral and derivative In this paper, the spectral approximations are used to compute the fractional integral and the Caputo derivative. The effective recursive formulae based on... C Li,F Zeng,F Liu - 《Fractional Calculus & Applied Analysis》 被引量: ...
A new equivalence of Stefan's problems for the Time-Fractional-Diffusion Equation A fractional Stefan's problem with a boundary convective condition is solved, where the fractional derivative of order α∈ (0, 1) is taken in the Caputo ... S Roscani,ES Marcus - 《Fractional Calculus & App...