We consider an optimal rearrangement maximization problem involving the fractional Laplace operator ( − Δ ) s , 0 < 1 and Gagliardo-Nirenberg seminorm [ u ] . prove existence of a maximizer, analyze its properties show that it satisfies unstable obstacle equation for some α > = χ { }

Nowadays, numerical models have great importance in every field of science, especially for solving the nonlinear differential equations, partial differential equations, biochemical reactions, etc. The total time evolution of the reactant concentrations in the basic enzyme-substrate reaction is simulated by the Runge-Kutta of order four (RK4) and by nonstandard finite difference (NSFD) method. A...

In this paper, a new numerical method for solving the fractional Riccati differential  equation is presented. The fractional derivatives are described in the Caputo sense. The method is based upon  fractional-order Bernoulli functions approximations. First, the  fractional-order Bernoulli functions and  their properties are  presented. Then, an operational matrix of fractional order integration...

Many protein and mRNA species occur at low molecular counts within cells, and hence are subject to large stochastic fluctuations in copy numbers over time. Development of computationally tractable frameworks for modelling stochastic fluctuations in population counts is essential to understand how noise at the cellular level affects biological function and phenotype. We show that stochastic hybr...

We derive a fractional reaction–di usion equation from a continuous-time random walk model with temporal memory and sources. The equation provides a general model for reaction–di usion phenomena with anomalous di usion such as occurs in spatially inhomogeneous environments. As a rst investigation of this equation we consider the special case of single species fractional reaction–di usion in one...

In this paper, a computational intelligence method is used for the solution of fractional optimal control problems (FOCP)'s with equality and inequality constraints. According to the Ponteryagin minimum principle (PMP) for FOCP with fractional derivative in the Riemann- Liouville sense and by constructing a suitable error function, we define an unconstrained minimization problem. In the optimiz...

This paper deals with the application of fourth kind Chebyshev wavelets (FKCW) in solving numerically a model of HIV infection of CD4+T cells involving Caputo fractional derivative. The present problem is a system of nonlinear fractional differential equations. The goal is to approximate the solution in the form of FKCW truncated series. To do this, an operational matrix of fractional integrati...

In this paper, we integrate goal programming (GP), Taylor Series, Kuhn-Tucker conditions and Penalty Function approaches to solve linear fractional bi-level programming (LFBLP)problems. As we know, the Taylor Series is having the property of transforming fractional functions to a polynomial. In the present article by Taylor Series we obtain polynomial objective functions which are equivalent...