Abstract We consider time-changed Brownian motions on random Koch (pre-fractal and fractal) domains where the time change is given by inverse to a subordinator. In particular, we study fractional Cauchy problem with Robin condition pre-fractal boundary obtaining asymptotic results for corresponding diffusions Robin, Neumann Dirichlet conditions fractal domain.

We derive existence results for a parabolic bipolynomial abstract and classical problems containing fractional powers of the Dirichlet-Laplace operator on bounded domain, in sense Stone-von Neumann calculus. The main tools are theorems uniqueness weak solutions to an problem, due Friedman, general theorem equivalence strong some equation.

Abstract In this paper we focus on the following nonlocal problem with critical growth: $$\begin{aligned} \left\{ \begin{array}{ll} (-\Delta )^{s} u = \lambda + u_{+}^{2^{*}_{s}-1} f(x) &amp;{} \text{ in } \Omega ,\\ u=0 \mathbb {R}^{N}\setminus , \end{array} \right. \end{aligned}$$ <mml:mfence...

in this paper, we prove the existence of the solution for boundary value prob-lem(bvp) of fractional dierential equations of order q 2 (2; 3]. the kras-noselskii&apos;s xed point theorem is applied to establish the results. in addition,we give an detailed example to demonstrate the main result.

Optimization of the ratio of two functions is called fractional programming or ratio optimization problem. If one can optimize simultaneously collection of fractional objective functions then the problem is called multi-objective fractional programming. This paper presents a survey on fractional programming problems. In contrast, this survey excludes many of the technical details and provides a...

The sum of a fractional program is a nonconvex optimization problem in the field of fractional programming and it is difficult to solve. The development of research is restricted to single objective sums of fractional problems only. The branch and bound methods/algorithms are developed in the literature for this problem as a single objective problem. The theoretical and algorithmic development ...