n this paper, at first the  concept of caputo fractionalderivative is generalized on time scales. then the fractional orderdifferential equations are introduced on time scales. finally,sufficient and necessary conditions are presented for the existenceand uniqueness of solution of initial valueproblem including fractional order differential equations.

this paper studies the existence of solutions for acoupled system of nonlinear fractional differential equations. newexistence and uniqueness results are established using banach fixedpoint theorem. other existence results are obtained using schaeferand krasnoselskii fixed point theorems. some illustrative examplesare also presented.

in this article using the inverse laplace transform, we show analytical solutions for the generalized mass transfers with (and without) a chemical reaction. these transfers have been expressed as the couette flow with the fractional derivative of the caputo sense. also, using the hankel contour for the bromwich's integral, the solutions are given in terms of the generalized airy functions.

in recent years, some statisticians have studied the signal detection problem by using the random field theory. in this paper we have considered point estimation of the gaussian scale space random field parameters in the bayesian approach. since the posterior distribution for the parameters of interest dose not have a closed form, we introduce the markov chain monte carlo (mcmc) algorithm to ap...

and Applied Analysis 3 2. Results Solutions to 1.1 subject to conditions 1.2 are meant in the following weak sense. Definition 2.1. A function u ∈ Lmloc Q ∩ L p loc Q is called a weak solution to 1.1 if ∫ Q |u|φ dP ∫ S u 0, t2;x φ 0, t2;x dP2 ∫ S u t1, 0;x φ t1, 0;x dP1 − ∫

Let A be a function with derivatives of order m and DγA∈ Λ̇β (0 < β < 1, |γ| =m). The authors in the paper proved that ifΩ∈ Ls(Sn−1) (s≥ n/(n−β)) is homogeneous of degree zero and satisfies a vanishing condition, then both the higher-order Marcinkiewicz-type integral μΩ and its variation μ̃ A Ω are bounded from L p(Rn) to Lq(Rn) and from L1(Rn) to Ln/(n−β),∞(Rn), where 1 < p < n/β and 1/q = 1/p− ...

In this paper we describe the derivations of orthosymplectic Lie superalgebras over a superring. In particular, we derive sufficient conditions under which the derivations can be expressed as a semidirect product of inner and outer derivations. We then present some examples for which these conditions hold.

We give a complete characterization of those f : [0, 1] → X (where X is a Banach space which admits an equivalent Fréchet smooth norm) which allow an equivalent C 2 parametrization. For X = R, a characterization is well-known. However, even in the case X = R 2 , several quite new ideas are needed. Moreover, the very close case of parametrizations with a bounded second derivative is solved.

Here, Ω is a bounded domain with sufficiently smooth (e.g. Lipschitz) boundary ∂Ω and ∂/∂ν denotes the (outward) normal derivative on ∂Ω. We assume that the function φ :R→R, defined by φ(s)= α(|s|)s if s = 0 and 0 otherwise, is an increasing homeomorphism from R to R. Let Φ(s)= ∫ s 0 φ(t)dt, s∈R. Then Φ is a Young function. We denote by LΦ the Orlicz space associated withΦ and by ‖ · ‖Φ the usu...