On the application of the homotopy analysis method for a nonlocal mixed problem with Bessel operator

In this research work, we give analytic approximate solutions for a nonlocal initial boundary value problem where one of the classical conditions is replaced by an integral condition by employing the homotopy analysis method (HAM). The series solution can be obtained by either using initial conditions (partial t-solution) or by using the boundary conditions (partial x-solution). This method allows us to control the convergence region of the series solution.