In this work, a non-integer order Airy equation involving Liouville differential operator is considered. Proposing an undetermined integral solution to the left fractional Airy differential equation, we utilize some basic fractional calculus tools to clarify the closed form. A similar suggestion to the right FADE, converts it into an equation in the Laplace domain. An illustration t...

The present paper is devoted to constructing L2 type difference analog of the Caputo fractional derivative. fundamental features this operator are studied and it used construct schemes generating approximations second fourth order in space (3−α)th-order time for diffusion equation with variable coefficients. Difference were also constructed variable-order generalized fractional-order Sobolev ty...

The cable equation is a second order, parabolic, partial differential equation that describes the evolution of voltage in the dendrite of a neuron. Here we look at the various ways in which lambda ( space constant/variable space constant/ length parameter ) is calculated in the cases of linear, passive transmission as well as nonlinear active transmission. Changes in morphology are taken into a...

in this paper, operational matrices of riemann-liouville fractional integration and caputo fractional differentiation for shifted jacobi polynomials are considered. using the given initial conditions, we transform the fractional differential equation (fde) into a modified fractional differential equation with zero initial conditions. next, all the existing functions in modified differential equ...

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 ...

The stable difference scheme for the approximate solution of the initial value problem ( ) ( ) ( ) ( ) 1 2 , t du t D u t Au t f t dt + + = ( ) 0 1, 0 0 t u < < = for the differential equation in a Banach space E with the strongly positive operator A and fractional operator 1 2 t D is presented. The well-posedness of the difference scheme in difference analogues of spaces of smooth functions is...

In this paper, a new spectral-iterative method is employed to give approximate solutions of fractional logistic differential equation. This approach is based on combination of two different methods, i.e. the iterative method cite{35} and the spectral method. The method reduces the differential equation to systems of linear algebraic equations and then the resulting systems are solved by a numer...

The stable difference scheme for the approximate solution of the initial value problem du(t) dt + D 1 2 t u(t) + Au(t) = f(t), 0 < t < 1, u(0) = 0 for the differential equation in a Banach space E with the strongly positive operator A and fractional operator D 1 2 t is presented. The well-posedness of the difference scheme in difference analogues of spaces of smooth functions is established. In...

A new homotopy perturbation method (NHPM) is applied to system of variable coefficient coupled Burgers' equation with time-fractional derivative. The fractional derivatives are described in the Caputo fractional derivative sense. The concept of new algorithm is introduced briefly, and NHPM is examined for two systems of nonlinear Burgers' equation. In this approach, the solution is considered a...