#FX EQUATION 5 SERIES#
KEYWORDS Fractional calculus laplace transform laplace residual power series method fractional partial differential equation power series fractional power series 1 Introduction Fairouz Tchier,Hassan Khan,Shahbaz Khan,Poom Kumam and Ioannis DassiosġMathematics Department,King Saudi University,Riyadh,145111,Saudi ArabiaĢDepartment of Mathematics,Abdul Wali Khan University,Mardan,23200,PakistanģDepartment of Mathematics,Near East University,Nicosia,99138,TurkeyĤTheoretical and Computational Science(TaCS)Center Department of Mathematics,Faculty of Science,King Mongkuts University of Technology Thonburi(KMUTT),Bangkok,10140,ThailandĥDepartment of Medical Research,China Medical University Hospital,China Medical University,Taichung,40402,TaiwanĦAMPSAS,University College Dublin,Dublin,A94 XF34,IrelandĪBSTRACT The nonlinearity in many problems occurs because of the complexity of the given physical phenomena.The present paper investigates the non-linear fractional partial differential equations’solutions using the Caputo operator with Laplace residual power series method.It is found that the present technique has a direct and simple implementation to solve the targeted problems.The comparison of the obtained solutions has been done with actual solutions to the problems.The fractional-order solutions are presented and considered to be the focal point of this research article.The results of the proposed technique are highly accurate and provide useful information about the actual dynamics of each problem.Because of the simple implementation,the present technique can be extended to solve other important fractional order problems.
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