Surfaces with Prescribed Nodes and Minimum Energy Integral of Fractional Order

his paper presents a method of finding a continuous, real-valued, function of two variables z = u(x,y) defined on the square S := [0,1]^2, which minimizes an energy integral of fractional order, subject to the condition u(0,y) = u(1,y) = u(x,0) = u(x,1) = 0 and u(x_i,y_j) = c_{ij}, where 0 < x_1 < ... < x_M < 1, 0 < y_1 < ... є ℝ are given. The function is expressed as a double Fourier sine series, and an iterative procedure to obtain the function will be presented