Numerical Solutions of Fractional-Order Electrical RLC Circuit Equations via Three Numerical Techniques

Numerical solutions for fractional reaction-diffusion equations

Fractional diffusion equations are useful for applications where a cloud of particles spreads faster than the classical equation predicts. In a fractional diffusion equation, the second derivative in the spatial variable is replaced by a fractional derivative of order less than two. The resulting solutions spread faster than the classical solutions and may exhibit asymmetry, depending on the fr...

Numerical Solutions to Fractional Perturbed Volterra Equations

and Applied Analysis 3 where Θ is a weight function, is called the scalar product of functions f, g on the interval 0, t . Let us recall that two functions are orthonormal when ∀i,j 〈 φi t , φj t 〉 δij , 2.2 where δij is the Kronecker delta. We are looking for an approximate solution to 1.1 as an element of the subspaceHnφ , spanned on nφ first basic functions {φj : j 1, 2, . . . , nφ} unφ x, t...

numerical solution of multi-order fractional differential equations via the sinc collocation method

in this paper, the sinc collocation method is proposed for solving linear and nonlinear multi-order fractional differential equations based on the new definition of fractional derivative which is recently presented by khalil, r., al horani, m., yousef, a. and sababeh, m. in a new definition of fractional derivative, j. comput. appl. math. 264 (2014), 65{70. the properties of sinc functions are ...

Numerical and Analytical Treatment of Differential Equations of Fractional Order

Numerical Solutions of a Variable-Order Fractional Financial System

The numerical solution of a variable-order fractional financial system is calculated by using the Adams-Bashforth-Moulton method. The derivative is defined in the Caputo variable-order fractional sense. Numerical examples show that the Adams-Bashforth-Moulton method can be applied to solve such variable-order fractional differential equations simply and effectively. The convergent order of the ...