Keywords: Schauder fixed point principle Exponentially stable Acquistapace–Terreni conditions Evolution families Almost periodic Higher-order differential equation with operator coefficients Wave equation with fractional damping a b s t r a c t In this paper, we make extensive use of the well-known Schauder fixed point principle and the exponential stability of the evolution family involved to ...

The present study introduces a new version of homotopy perturbation method for the solution of system of fractional-order differential equations. In this approach, the solution is considered as a Taylor series expansion that converges rapidly to the nonlinear problem. The systems include fractional-order stiff system, the fractional-order Genesio system, and the fractional-order matrix Riccati-...

High-order methods inspired by the multi-step Adams methods are proposed for systems of fractional differential equations. The schemes are based on an expansion in a weighted L space. To obtain the schemes this expansion is terminated after P + 1 terms. We study the local truncation error and its behavior with respect to the step-size h and P . Building on this analysis, we develop an error ind...

The motion differential equation of hydro-pneumatic suspension is established to describe the vibration characteristics for a certain type construction vehicle. output force was deduced from parameters. Based on multi-phase medium, fractional calculus theory introduced, and its Bagley–Torvik formed. numerical computation by low-pass filter Oustaloup algorithm performed. solution nonlinear obtai...

We consider the numerical solution of the Bagley-Torvik equation Ay′′(t) + BD ∗ y(t) + Cy(t) = f(t) as a prototype fractional differential equation with two derivatives. Approximate solutions have recently been proposed in the book and papers of Podlubny in which the solution obtained with approximate methods is compared to the exact solution. In this paper we consider the reformulation of the ...

In this paper, the ( / ) G G  -expansion method is extended to solve fractional differential equations in the sense of modified Riemann-Liouville derivative. Based on a nonlinear fractional complex transformation, certain fractional partial differential equations can be turned into ordinary differential equations of integer order. For illustrating the validity of this method, we apply it to fi...

Numerical methods are used to find exact solution for the nonlinear differential equations. In the last decades Iterative methods have been used for solving fractional differential equations. In this paper, the Homotopy perturbation method has been successively applied for finding approximate analytical solutions of the fractional nonlinear Klein–Gordon equation can be used as numerical algorit...

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...

Fractional order partial differential equations are generalizations of classical partial differential equations. Increasingly, these models are used in applications such as fluid flow, finance and others. In this paper we examine some practical numerical methods to solve a class of initial- boundary value fractional partial differential equations with variable coefficients on a finite domain. S...

This paper deals with impulsive fractional differential inclusions with a fractional order multi-point boundary condition and with fractional order impulses. By use of multi-valued analysis and topological fixed point theory, we present some existence results under both convexity and nonconvexity conditions on the multi-valued right-hand side. The compactness of the solutions set and continuous...