Ntamack, "Solutions of the Klein-Gordon Equation with the Hulthen Potential Using the Frobenius Method
," International Journal of Theoretical and Mathematical Physics, vol.
A transfer matrix method and the Frobenius method
were adopted by J.
Frobenius Method. In this work to perform the Frobenius method, we consider the groundwater flow governed by the following fractional Caputo-Weyl derivation partial differential of order 2[alpha], where [alpha] is real number, 0 < [alpha] [less than or equal to] 1.
To meet the condition under which Frobenius method can be used, we have to prove that p(r) and q(r) are analytical around [r.sub.b] that means we have to prove that p(r) and q(r) can be written as series.
From the above expression we can see that p(r) and q(r) are analytical around [r.sub.b], which follows from Frobenius method that the solution of (15) can be in the form
In the following section the analytical asymptotic solution obtained in Laplace space via Frobenius method will be compared with the experimental data.
The problem of the aperiodic vibration of a beam with any curvature and a variable cross section was solved using the Frobenius method
combined with the dynamic stiffness method and the Laplace transformation in Huang et al.
We solve equations (14) and (15) by using Frobenius method
for second order differential equation.
The general method for solving these equations is the Frobenius method
, which requires approximating displacements in terms of power series which are functions of x , substituting in the respective equations and applying boundary conditions in order to calculate the constants.
In section 4 we use the Frobenius Method to solve differential equations in the neighborhood of a singular regular point.
In the Frobenius Method we look for the solution in the form y = [[infinity].summation over (n=0)] [a.sub.n][x.sup.n+r].
To solve the equation 2[x.sup.2]y" - xy' + (1 + [x.sup.2]) y = 0 using the Frobenius method, we take P = 2[x.sup.2], Q = -x, R = 1 + [x.sup.2] and find the roots of the Indicial equation using the program "Indicial".