Multiple solutions for fractional differential equations: Analytic approach

Multiple solutions of the fractional differential equations is an interesting subject in the area of mathematics, sciences and engineering. A new Algorithm for finding multiple solution of fractional differential equations is constructed based on a homotopy map between initial approximation and exact solution with predictor force condition. Easy and efficient algorithm is introduced to approximate the multiple solutions, even if these multiple solutions are very close and thus rather difficult to distinct even by numerical techniques. Several examples are presented to demonstrate the efficiency of the algorithm. To the best of our knowledge, we present multiple solutions for fractional differential equations analytically.