In this paper, biochemical reaction problem is given in the form of a system of non-linear differential equations involving Caputo fractional derivative. The aim is to suggest an instrumental scheme to approximate the solution of this problem. To achieve this goal, the fractional derivation terms are expanded as the elements of shifted Legendre scaling functions. Then, applying operational matr...

In recent years, many works on the subject of fractional calculus contain interesting accounts of the theory and applications of fractional calculus operators in a number of areas of mathematical analysis ( such as ordinary and partial differential equations, integral equations, summation of series, etc.). The main object of this paper is to construct multivariable extension of Jacobi polynomia...

in recent years, there has been greater attempt to find numerical solutions of differential equations using wavelet's methods. the following method is based on vector forms of haar-wavelet functions. in this paper, we will introduce one dimensional haar-wavelet functions and the haar-wavelet operational matrices of the fractional order integration. also the haar-wavelet operational matrice...

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...

By using the coincidence degree theory, we consider the following 2m-point boundary value problem for fractional differential equationD 0 u t f t, u t , D α−1 0 u t , D α−2 0 u t e t , 0 < t < 1, I3−α 0 u t |t 0 0, Dα−2 0 u 1 ∑m−2 i 1 aiD α−2 0 u ξi , u 1 ∑m−2 i 1 biu ηi , where 2 < α ≤ 3, D 0 and I 0 are the standard Riemann-Liouville fractional derivative and fractional integral, respectively...

ABSTRACT. In this paper, Ulam stability and data dependence for fractional differential equations with Caputo fractional derivative of order α are studied. We present four types of Ulam stability results for the fractional differential equation in the case of 0 < α < 1 and b = +∞ by virtue of the Henry-Gronwall inequality. Meanwhile, we give an interesting data dependence results for the fracti...

Based on the bifurcation diagram technique, this paper analyses the stabilization conditions of the nonlinear chaotic Genesio-Tesi system with the use of a fractional order control scheme. Stability analysis is performed for the closedloop nonlinear chaotic system behavior, for the fractional order integral and derivative actions by mean of the bifurcation diagram. Numerical simulation examples...

The paper presents development of a new tuning method for fractional order PID controller for the systems which have integer order transfer functions. All the parameters of the controller, namely proportional gain kp, integral gain ki, derivative gain kd, fractional order of integrator λ and fractional order of differentiator μ can be obtained by using this method. It is clearly shown that the ...

some preliminaries about the integrable families of riccati equations and solutions structure of these equations in several cases are presented in this paper, then by using of definitions for fractional derivative we apply the new extended of tanh method to the perturbed nonlinear fractional schrodinger equation with the kerr law nonlinearity. finally by using of this method and solutions of ri...

in this paper, we use the riemann-liouville fractionalintegrals to establish some new integral inequalities related tochebyshev's functional in the case of two differentiable functions.