@article{MAKHILLJEAS2017121914846,
    title = {The Effect of Surface Pressure and Elasticity to the Surface
Minimum Energy with Fractional Order},
    journal = {Journal of Engineering and Applied Sciences},
    volume = {12},
    number = {19},
    pages = {4851-4855},
    year = {2017},
    issn = {1816-949x},
    doi = {jeasci.2017.4851.4855},
    url = {https://makhillpublications.co/view-article.php?issn=1816-949x&doi=jeasci.2017.4851.4855},
    author = {E.,E.,K.,S. and},
    keywords = {Minimization,surface energy,fractional order,elasticity,regression models,operator},
    abstract = {Minimization and saving are two key words that currently often related to the solution of energy
problem. In this study, we discuss the fact that when an elastic flat surface is pressed from the bottom at some
points then a potential energy is formed at any points on the surface towards the bottom of the surface which
is called the surface energy. The problem addressed in this study is to determine the functional relationship
between the minimum surface energy with the value of the surface elasticity and the value of the pressure. In
the previous research, the surface can be represented as a function of two variables in the form of double sine
series. In this case, the energy is defined as the integral of the square of the Laplace operator with the order of
the derivative generalized into fractional value. The pressure is the value of function at the pressed point
coordinates while elasticity is the value of the fractional order. Some values of the minimum energy which
depend on the surface elasticity, pressure and pressure point coordinates are used as the data to obtain a
regression model of the functional relationship. Knowing the relationship between the involved varaiables, the
resulting regression model can be used to determine the minimum energy easily. The model reveals that the
coordinates of the pressure point does not significantly affect the surface energy. The surface energy is only
depend on the pressure and surface elasticity.}
    }