New Derivatives on Fractal Subset of Real-line

In this manuscript we introduced the generalized fractional Riemann-Liouville and Caputo like derivative for functions defined on fractal sets. The Gamma, Mittag-Leffler and Beta functions were defined on the fractal sets. The non-local Laplace transformation is given and applied for solving linear and non-linear fractal equations. The advantage of using these new nonlocal derivatives on fractals subset of real-line lies in the fact that they are used for better modelling of processes with memory effect

Diffusion on middle-ξ\xi Cantor sets

In this paper, we study $C^{\zeta}$-calculus on generalized Cantor sets, which have self-similar properties and fractional dimensions that exceed their topological dimensions. Functions with fractal support are not differentiable or integrable in terms of standard calculus, so we must involve local fractional derivatives. We have generalized the $C^{\zeta}$-calculus on the generalized Cantor sets known as middle-$\xi$ Cantor sets. We have suggested a calculus on the middle-$\xi$ Cantor sets for different values of $\xi$ with $0<\xi<1$. Differential equations on the middle-$\xi$ Cantor sets have been solved, and we have presented the results using illustrative examples. The conditions for super-, normal, and sub-diffusion on fractal sets are given.Comment: 15 pages, 11 figure

Solving and Applying Fractal Differential Equations: Exploring Fractal Calculus in Theory and Practice

In this paper, we delve into the fascinating realm of fractal calculus applied to fractal sets and fractal curves. Our study includes an exploration of the method analogues of the separable method and the integrating factor technique for solving $\alpha$-order differential equations. Notably, we extend our analysis to solve Fractal Bernoulli differential equations. The applications of our findings are then showcased through the solutions of problems such as fractal compound interest, the escape velocity of the earth in fractal space and time, and estimation of time of death incorporating fractal time. Visual representations of our results are also provided to enhance understanding

The role of human factor in incidence and severity of road crashes based on the CART and LR regression: a data mining approach

AbstractAccidents are one of the biggest public health problems in the world. As literature indicated, the traffic accidents were assessed to be most significant health problem in Iran. To date, no serious researches have analyzed high dimensional traffic data In Iran. This paper, therefore, aims to bridge the gap. In this study, the traffic data are analyzed by Data Mining techniques such as Logistic Regression, Classification and Regression Trees. In this paper the impact of such factors were investigated using these techniques. It is hoped that the current research findings will help governments in better road designs and traffic management

AN IFC-BASED FRAMEWORK FOR OPTIMIZING LEVEL OF PREFABRICATION IN INDUSTRIALIZED BUILDING SYSTEMS

Ph.DDOCTOR OF PHILOSOPH

A new model for probabilistic multi-period multi-objective project selection problem

The project selection problem is considered as one of the most imperative decisions for investor organizations. Due to non-deterministic nature of some criteria in the real world projects in this paper, a new model for project selection problem is proposed in which some parameters are assumed probabilistic. This model is formulated as a non-linear, multi-objective, multi-period, zero-one programming model. Then the epsilon constraint method and an algorithm are applied to check the Pareto front and to find optimal solutions. A case study is conducted to illustrate the applicability and effectiveness of the approach, with the results presented and analysed. Since the proposed model is more compatible with real world problems, the results are more tangible and trustable compared with deterministic cases. Implications of the proposed approach are discussed and suggestions for further work are outlined