‎in this paper‎, ‎we provide sufficient conditions for the existence of nonnegative solutions of a boundary value problem for a fractional order differential equation‎. ‎by applying kranoselskii`s fixed--point theorem in a cone‎, ‎first we prove the existence of solutions of an auxiliary bvp formulated by truncating the response function‎. ‎then the arzela--ascoli theorem is used to take $c^1$ ...

Abstract In this paper, we consider a class of fractional boundary value problems with the derivative term and nonlinear operator term. By establishing new mixed monotone fixed point theorems, prove these to have unique solution, construct corresponding iterative sequences approximate solution.

in this paper we introduce a type of fractional-order polynomials basedon the classical chebyshev polynomials of the second kind (fcss). also we construct the operationalmatrix of fractional derivative of order $ gamma $ in the caputo for fcss and show that this matrix with the tau method are utilized to reduce the solution of some fractional-order differential equations.

Let Ω be a C2-bounded domain of Rd, d = 2, 3, and fix Q = (0, T )×Ω with T ∈ (0,+∞]. In the present paper we consider a Dirichlet initial-boundary value problem associated to the semilinear fractional wave equation ∂α t u + Au = fb(u) in Q where 1 < α < 2, ∂α t corresponds to the Caputo fractional derivative of order α, A is an elliptic operator and the nonlinearity fb ∈ C1(R) satisfies fb(0) =...

In this article, we develop the distributed order fractional hybrid differential equations (DOFHDEs) with linear perturbations involving the fractional Riemann-Liouville derivative of order $0 < q < 1$ with respect to a nonnegative density function. Furthermore, an existence theorem for the fractional hybrid differential equations of distributed order is proved under the mixed $varphi$-Lipschit...

A fractional wave equation with a Riemann–Liouville derivative is considered. An arbitrary self-adjoint operator discrete spectrum was taken as the elliptic part. We studied inverse problem of determining order time derivative. By setting value projection solution onto first eigenfunction at fixed point in an additional condition, uniquely restored. The abstract allows us to include many models...

This paper presents an analytical technique for the analysis of a stochastic dynamic system whose damping behavior is described by a fractional derivative of order 1/2. In this approach, an eigenvector expansion method proposed by Suarez and Shokooh is used to obtain the response of the system. The properties of Laplace transforms of convolution integrals are used to write a set of general Duha...

A numerical method to solve the fractional diffusion equation, which could also be easily extended to many other fractional dynamics equations, is considered. These fractional equations have been proposed in order to describe anomalous transport characterized by non-Markovian kinetics and the breakdown of Fick’s law. In this paper we combine the forward time centered space (FTCS) method, well k...

A numerical method to solve the fractional diffusion equation, which could also be easily extended to many other fractional dynamics equations, is considered. These fractional equations have been proposed in order to describe anomalous transport characterized by non-Markovian kinetics and the breakdown of Fick’s law. In this paper we combine the forward time centered space (FTCS) method, well k...