On the Solution of the Fractional Quintic Generalized Complex Ginzburg‐Landau Equation Using an Accurate and Direct Procedure

ABSTRACT In the present paper, an efficient and direct technique is implemented to determine the generalized quintic complex Ginzburg‐Landau (GCGL) equations. The nonlinearity in the targeted problems is directly handled by utilizing the proposed technique. The fractional derivative is expressed in term of Caputo definition. Two numerical examples of complex nature are considered to justify the applicability and validity of the recommended technique. First, the fractional GCGL equations are separated into real and imaginary parts, which results in the system of fractional partial differential equations (FPDEs). The 2D and 3D graphical representations of LRPSM and exact solutions are done for the solution of both fractional and integer order problems. It is observed that the exact solution of each problem is in good contact with the integer‐order LRPSM solution. It is further examined that the LRPSM solution with greater terms has higher accuracy as compared to the solution with fewer terms.