A Second Order Fuzzy Differential Equation for The Case of A Semi-Confined Aquifer

Christos Tzimopoulos, Christos Evangelides, Kyriakos Papadopoulos, Basil Papadopoulos

Differential equations are encountered very often in engineering problems and generally in al sciences. Modeling the effect of variation of physical quantities such as temperature, pressure, velocity, stress, strain, current moisture and many other on engineering problems requires most of the times the establishment of differential equations. For simplicity reason the parameters and variables involved which are measured or estimated from experience are considered exact even though they often contain uncertainties. One way do deal with these uncertainties nowadays is through convex fuzzy sets. According to all the above it is almost unavoidable to introduce fuzzy parameters and variables in the solution of differential equations. Much research was carried out during the recent years in theoretic and applied subjects containing fuzzy differential equations with H-derivative. This method though, in some cases has some disadvantages leading to solutions with increasing support as time t increases. In order to alleviate this disadvantage the generalized differentiability (G-H derivative) was introduced. In this paper the case of a semi-confined aquifer is studied, which is bounded on top by a thin semi-permeable layer and on bottom by an impermeable layer. This system leads to a second order differential equation with fuzzy boundary. The solution of this problem is obtained using the generalized H-derivative.