in this paper, we prove the existence and uniqueness results to the random fractional functional differential equations under assumptions more general than the lipschitz type condition. moreover, the distance between exact solution and appropriate solution, and the existence extremal solution of the problem is also considered.

The paper is devoted to study analogues of the van der Corput lemmas involving Mittag-Leffler functions. generalisation that we replace exponential function with Mittag-Leffler-type function, oscillatory integrals appearing in analysis time-fractional partial differential equations. More specifically, integral form I?,?(?)=?RE?,?(i???(x))?(x)dx, for range 00. This extends variety estimat...

We investigate the stability properties of strongly continuous semigroups generated by operators form $A-BB^\ast$, where $A$ is a generator contraction semigroup and $B$ possibly unbounded operator. Such systems arise naturally in study hyperbolic partial differential equations with damping on boundary or inside spatial domain. As our main results we present general sufficient conditions for no...

the complex-step derivative approximation is applied to compute numerical derivatives. in this study, we propose a new formula of fractional complex-step method utilizing jumarie definition. based on this method, we illustrated an approximate analytic solution for the fractional cauchy-euler equations. application in image denoising is imposed by introducing a new fractional mask depending on s...

We consider the possibility of gauge bosons living in the recently proposed fivedimensional theory with localized gravity. We study the mass spectrum of the Kaluza-Klein (KK) excitations of the gauge fields and calculate their couplings to the boundaries of the fifth dimension. We find a different behaviour from the case of the graviton. In particular, we find that the massless mode is not loca...