This paper is devoted to the controlled drift estimation of mixed fractional Ornstein-Uhlenbeck process. We will consider two models: one optimal input where we find function which maximize Fisher information for unknown parameter and other with a constant as function. Large sample asymptotical properties Maximum Likelihood Estimator (MLE) deduced using Laplace transform computations or Cameron...

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 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...

In this paper author has obtained the neutrix product of x+ −r and δ (α) (x), where α is a positive fractional number. Key Words: Neutrix limit, fractional-differentiation, sequence, function. Ams Subject Classification- 46F 1. INTRODUCTION N defined by J.G. vander Corput [2] as commutative additive group functions ν(ξ) on domain N' with values in N", further if for some ν N, = γ all ξ N', then...

This paper deals with the Cauchy problem for a nonlinear hyperbolic equation D1+α 0|t u+D 0|tu+ (− ) γ 2 u = h(t, x) | u |p| 1 − u |q, posed in Q = R+ × R, where pi, qi > 1, −1 < α < 1, 0 < β < 2, 0 < γ ≤ 2, and β < 1+α with given initial position and velocity u(x, 0) = u0(x), ut (x, 0) = u1(x), and the Cauchy problem for a nonlinear hyperbolic system with initial data   D 1+α1 0|t...

‎it is commonly accepted that fractional differential equations play‎ ‎an important role in the explanation of many physical phenomena‎. ‎for‎ ‎this reason we need a reliable and efficient technique for the‎ ‎solution of fractional differential equations‎. ‎this paper deals with‎ ‎the numerical solution of a class of fractional differential‎ ‎equation‎. ‎the fractional derivatives are described...

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.