An algorithm for the numerical solution of differential equations of fractional order.
An almost-periodicity criterion for solutions of the oscillatory differential equation and its applications
The linear differential equation with the uniformly almost-periodic function is considered. Necessary and sufficient conditions which guarantee that all bounded (on ) solutions of are uniformly almost-periodic functions are presented. The conditions are stated by a phase of . Next, a class of equations of the type whose all non-trivial solutions are bounded and not uniformly almost-periodic is given. Finally, uniformly almost-periodic solutions of the non-homogeneous differential equations...
An analysis of the stability boundary for a linear fractional difference system
This paper deals with basic stability properties of a two-term linear autonomous fractional difference system involving the Riemann-Liouville difference. In particular, we focus on the case when eigenvalues of the system matrix lie on a boundary curve separating asymptotic stability and unstability regions. This issue was posed as an open problem in the paper J. Čermák, T. Kisela, and L. Nechvátal (2013). Thus, the paper completes the stability analysis of the corresponding fractional difference...
An angle metric through the notion of Grassmann representative.
An application of a global bifurcation theorem to the existence of solutions for integral inclusions.
An application of the antimaximum principle for a fourth order periodic problem.
An application of the dual variational principle to a Hamiltonian system with discontinuous nonlinearities.
An application of the Nash-Moser theorem to ordinary differential equations in Fréchet spaces
A general existence and uniqueness result of Picard-Lindelöf type is proved for ordinary differential equations in Fréchet spaces as an application of a generalized Nash-Moser implicit function theorem. Many examples show that the assumptions of the main result are natural. Applications are given for the Fréchet spaces , , , , for Köthe sequence spaces, and for the general class of subbinomic Fréchet algebras.
An approximation property for abstract differential equations
An efficient zero-stable numerical method for fourth-order differential equations.
An Epidemic Model With Post-Contact Prophylaxis of Distributed Length II. Stability and Oscillations if Treatment is Fully Effective
A possible control strategy against the spread of an infectious disease is the treatment with antimicrobials that are given prophylactically to those that had contact with an infective person. The treatment continues until recovery or until it becomes obvious that there was no infection in the first place. The model considers susceptible, treated uninfected exposed, treated infected, (untreated) infectious, and recovered individuals. The overly optimistic assumptions are made that treated uninfected...
An equation in the left and right fractional derivatives of the same order
An existence result for first order initial value problems for impulsive differential inclusions in Banach spaces
In this paper, a nonlinear alternative for multivalued maps is used to investigate the existence of solutions of first order impulsive initial value problem for differential inclusions in Banach spaces.
An existence result for nonlinear fractional differential equations on Banach spaces.
An existence theorem for differential inclusions on Banach space.
An existence theorem for fractional hybrid differential inclusions of Hadamard type
This paper studies the existence of solutions for fractional hybrid differential inclusions of Hadamard type by using a fixed point theorem due to Dhage. The main result is illustrated with the aid of an example.
An existence theorem for solutions of -th order nonlinear differential equations in the complex domain
An extended method of quasilinearization for nonlinear impulsive differential equations with a nonlinear three-point boundary condition.
An extension of Duhamel's integral to differential equations involving generalized functions; the steady-state solution
An extension of the method of quasilinearization
The method of quasilinearization is a well–known technique for obtaining approximate solutions of nonlinear differential equations. This method has recently been generalized and extended using less restrictive assumptions so as to apply to a larger class of differential equations. In this paper, we use this technique to nonlinear differential problems.