Sentence examples for fractional class from inspiring English sources

We first formulate a fractional class of explicit Adams Bashforth (A-B) and implicit Adams Moulton (A-M) methods of first- and second-order accuracy for the time-integration of Dtτ0Cu x,t)= g(t;u), τ∈ 0,1], where C0Dτt denotes the fractional derivative in the Caputo sense.

We introduced a technique based on a class of fractional differential stochastic equations (fractional Fokker-Planck equations) to discuss the fractional entropy solutions of fractional dynamical systems.

In the current study, we suggested symmetry of a class of fractional differential equations (the fractional calculus depends on the RL fractional operators) by utilizing its periodic solutions.

We research a class of fractional dynamical systems governed by fractional integrodifferential equations with nonlocal initial conditions.

We also establish certain conditions for the existence and uniqueness of solutions for such a class of fractional differential equations using Caputo fractional derivative.

This paper deals with the existence and approximate controllability for a class of fractional nonlocal control systems governed by abstract fractional evolution equations with multiple delays.

This paper concerns the boundary value problem of a class of fractional differential equations involving the Riemann-Liouville fractional derivative with nonlocal integral boundary conditions.

Liang and Yang [10] investigated the exact controllability for a class of fractional integro-differential control systems represented by nonlinear fractional evolution equations involving specific nonlocal functions.

Sakthivel et al. [14] studied the exact controllability for a class of fractional neutral control systems governed by abstract nonlinear fractional neutral evolution equations.

For fractional variational problems, which class of the fractional derivative is more effective?

For this purpose, a new class of fractional order Jacobi orthonormal functions is firstly introduced.