This paper concerns the dissipativity and stability of the Caputo nonlinear fractional functional differential equations (F-FDEs) with order 0 < α < 1. The fractional generalization of the Halanay-type inequality is proposed, which plays a central role in studies of stability and dissipativity of F-FDEs. Then the dissipativity and the absorbing set are derived under almost the same assumptions ...

We study the equivalences and implications between linear (or homogeneous) nth order fractional differential equations (FDEs) integral in spaces L1(a,b) C[a,b] when n≥ 2. establish equivalence of IVP FDE subject to initial condition u(i)(a)=ui for i {0,1,...,n-1} n≥2. The difficulty is that known conditions such first FDEs are not sufficient with In this article we provide additional ensure par...

Abstract In this manuscript, we examine both the existence and stability of solutions to implicit boundary value problem Caputo fractional differential equations variable order. We construct an example illustrate validity observed results.

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...

We consider both primal and dual formulations of singular autonomous systems three different types fractional-order differential equations. present a comprehensive study which proves that by using the spectrum linear pencil, polynomial matrix first order, not pencil prime system, we will receive information for all properties its system. In addition, this spectrum, solutions can be obtained for...

in this paper, a new fractional sub-equation method is proposed for finding exact solutions of fractional partial differential equations (fpdes) in the sense of modified riemann-liouville derivative. with the aid of symbolic computation, we choose the space-time fractional zakharov-kuznetsov-benjamin-bona-mahony (zkbbm) equation in mathematical physics with a source to illustrate the validity a...