in data envelopment analyze (dea) the scale efficiency in the input-oriented ccr model is less than or equal to the scale efficiency in dea based on the fractional analysis (dea-r). also, the scale efficiency in case of multiple inputs and one output and vice versa the scale efficiencies are equal in dea and dea-r. in this paper, first, dea-r model with weight restrictions when there is relativ...

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.

Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution....

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...

conclusions the use of smoothing methods helps us to eliminate non-linear effects but it is more appropriate to use cox proportional hazards model in medical data because of its’ ease of interpretation and capability of modeling both continuous and discrete covariates. also, cox proportional hazards model and smoothing methods analysis identified that age at diagnosis and tumor size were indepe...

The Keller-Segel model is a system of partial differential equations modelling chemotactic aggregation in cellular systems. This model has blowing up solutions for large enough initial conditions in dimensions d ≥ 2, but all the solutions are regular in one dimension; a mathematical fact that crucially affects the patterns that can form in the biological system. One of the strongest assumptions...

Fractional order diffusion equations are generalizations of classical diffusion equations which are used to model in physics, finance, engineering, etc. In this paper we present an implicit difference approximation by using the alternating directions implicit (ADI) approach to solve the two-dimensional space-time fractional diffusion equation (2DSTFDE) on a finite domain. Consistency, unconditi...

Education assessment is one of important measures that will be to ensure and continuously improve the educational level and educational quality. A fractional order model method for education evaluation is proposed in this paper. Improved fractional Basset force model is referred to constitute the complex education evaluation model. The detailed descriptions are displayed through building block ...