Anew Technique to Obtain Analytical Solutions for The Fractional Foam Drainage Formula

Abstract

In the present study, an innovative approach is proposed to solve a special case of fractional foam drainage using the Laplace residual power series technique (LRPS) in conjunction with the Caputo operator for determining the fractional derivative. The study provides extensive guidelines for utilizing this approach to solve time-fractional nonlinear formulas. The effectiveness and validity of the proposed method are investigated and established by comparing the obtained results with the accurate responses using graphs. The study also confirms that the accuracy of the proposed technique increases with the number of items in the combined solution of the problems, as demonstrated by the convergence of the correlation between the obtained solutions and the actual solutions for the special case of fractional foam drainage formula. The research findings suggest that the proposed technique is not only accurate and uncomplicated but also highly adaptable, making it suitable for addressing both linear and nonlinear situations.