Criteria of asymptotic ω-periodicity and their applications in a class of fractional differential equations

Periodicity and positivity of a class of fractional differential equations

Fractional differential equations have been discussed in this study. We utilize the Riemann-Liouville fractional calculus to implement it within the generalization of the well known class of differential equations. The Rayleigh differential equation has been generalized of fractional second order. The existence of periodic and positive outcome is established in a new method. The solution is des...

Periodicity in a System of Differential Equations with Finite Delay

The existence and uniqueness of a periodic solution of the system of differential equations d dt x(t) = A(t)x(t − ) are proved. In particular the Krasnoselskii’s fixed point theorem and the contraction mapping principle are used in the analysis. In addition, the notion of fundamental matrix solution coupled with Floquet theory is also employed.  

Existence of positive solution to a class of boundary value problems of fractional differential equations

This paper is devoted to the study of establishing sufficient conditions for existence and uniqueness of positive solution to a class of non-linear problems of fractional differential equations. The boundary conditions involved Riemann-Liouville fractional order derivative and integral. Further, the non-linear function $f$ contain fractional order derivative which produce extra complexity. Than...

On Type of Periodicity and Ergodicity to a Class of Fractional Order Differential Equations

Asymptotic Periodicity of Solutions to a Class of Neutral Functional Differential Equations

In this paper, we extend a convergence result due to Takác to continuous maps satisfying certain monotonicity properties. Applying this extension to the Poincaré map associated with the neutral equation (d/dt)[x(t) b(t)x(t r)] = F[t, x(t), x(t r>] we prove that each solution of the above neutral equation tends to an r-periodic function as ; —» oo in an oscillatory manner, where 0 < b(t) < 1 is ...