Abstract. In this paper, we introduce a new class of functions which are analytic and univalent with negative coefficients defined by using certain fractional operators descibed in the Caputo sense. Characterization property, the results on modified Hadamard product and integral transforms are discussed. Further, distortion theorem and radii of starlikeness and convexity are also determined here.

In this work we study integral boundary value problem involving Caputo differentiation  cD tu(t) = f(t, u(t)), 0 < t < 1, αu(0)− βu(1) = ∫ 1 0 h(t)u(t)dt, γu′(0)− δu′(1) = ∫ 1 0 g(t)u(t)dt, where α, β, γ, δ are constants with α > β > 0, γ > δ > 0, f ∈ C([0, 1]×R+,R), g, h ∈ C([0, 1],R+) and cD t is the standard Caputo fractional derivative of fractional order q(1 < q < 2). By using some fix...

We propose a new analysis tool for signals, called signature, that is based on complex wavelet signs. The complexvalued signature of a signal at some spatial location is defined as the fine-scale limit of the signs of its complex wavelet coefficients. We show that the signature equals zero at sufficiently regular points of a signal whereas at salient features, such as jumps or cusps, it is non-...

In this paper some embedding theorems related to fractional integration and differentiation in harmonic mixed norm spaces h(p, q, α) on the half-space are established. We prove that mixed norm is equivalent to a “fractional derivative norm” and that harmonic conjugation is bounded in h(p, q, α) for the range 0 < p ≤ ∞, 0 < q ≤ ∞. As an application of the above, we give a characterization of h(p...

Exploring the possible links between the mathematical field of fractional calculus and the electromagnetic theory has been one of the topics of our research interests in recent years. We have studied the possibility of bringing the tools of fractional calculus and electromagnetic theory together, and have explored and developed the topic of fractional paradigm in electromagnetic theory (see e.g...

A high-speed algorithm for computing fractional differentiations and fractional integrations in fractional differential equations is proposed. In this algorithm, the stored data are not the function to be differentiated or integrated but the weighted integrals of the function. The intervals of integration for the memory can be increased without loss of accuracy as the computing time-step n incr...

This paper proposes a new structure and substantiates the choice of technique for controller design using fractional integration differentiation. The method is based on extrapolation series integrating differentiating links, time constant which changes symmetrically from one step to another. does not contain three traditional links (proportional, integrating, differentiating) but contains six a...

in this article, we survey the asymptotic stability analysis of fractional differential systems with the prabhakar fractional derivatives. we present the stability regions for these types of fractional differential systems. a brief comparison with the stability aspects of fractional differential systems in the sense of riemann-liouville fractional derivatives is also given.

in this paper, boundary value problems of fractional order are converted into an optimal control problems. then an approximate solution is constructed from translations and dilations of a b-spline function such that the exact boundary conditions are satisfied. the fractional differential operators are taken in the riemann-liouville and caputo sense. several example are given and the optimal err...