where D , D , and D are the standard Riemann-Liouville fractional derivatives, I and I are the Riemann-Liouville fractional integrals, and 0 < γ < 1 < β < 2 < α < 3, ν,ω > 0, 0 < η, ξ < 1, k ∈R, f ∈ C([0, 1]×R×R,R), g ∈ C([0, 1]×R,R). The p-Laplacian operator is defined as φp(t) = |t|p–2t, p > 1, and (φp) = φq, 1 p + 1 q = 1. The study of boundary value problems in the setting of fractional cal...

In this paper, we introduce the class Ao (p,A,B, α ) of p-valent functions in the unit disc U = { z : | z | < 1 }. We obtain coefficient estimate, distortion and closure theorems, radii of close-to convexity, starlikeness and convexity of order δ ( 0 6 δ < 1 ) for this class. We also obtain class preserving integral operators for this class. Furthermore, various distortion inequalities for frac...

the aim of this paper is to design a fractional order sliding mode controllers (fosmc)for a class of dc-dc converters such as boost and buck converters. firstly, the control lawis designed with respect to the properties of fractional calculus, the design yields an equiv-alent control term with an addition of discontinuous (attractive) control law. secondly, themathematical proof of the stabilit...

Peter Bates (Michigan State University) Spectral convergence and Turing instability in systems with long range diffusion Abstract: Many physical and biological processes occur with long range interaction, giving rise to equations with nonlocal in space operators in place of the usual Laplacian. These operators are diffusive-like but are bounded rather than unbounded as is the case of the diffus...

Abstract We study fractional differential equations of Riemann–Liouville and Caputo type in Hilbert spaces. Using exponentially weighted spaces functions defined on $${\mathbb {R}}$$ R , we define operators by means a functional calculus using the Fourier transform. Main tools are extrapolation- interpolation...