Numerical Solution of Linear/Nonlinear Fractional Order Differential Equations Using Jacobi Operational Matrix

  • Shubham JaiswalEmail author
  • S. Das
Original Paper


During modeling of many physical problems and engineering processes, fractional differential equation (FDE) plays an important role. So an effective technique is required to solve such types of FDEs. Here, a new algorithm is proposed to solve various space fractional order reaction-convection–diffusion models. In the proposed approach shifted Jacobi polynomials are considered together with shifted Jacobi operational matrix of fractional order. The method is simple and effective to solve the linear as well as non-linear FDEs. A comparison between the numerical results of five existing problems and their analytical results through error analysis has been given to show the high accuracy, efficiency, and reliability of our proposed numerical method.


Fractional differential equations Jacobi polynomials Operational matrix Collocation method 



The present research work is carried out with financial support provided by the Department of Atomic Energy, Board of Research in Nuclear Sciences, Bhabha Atomic Research Centre, Mumbai, India.


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Copyright information

© Springer Nature India Private Limited 2019

Authors and Affiliations

  1. 1.Department of Mathematical SciencesIndian Institute of Technology (Banaras Hindu University)VaranasiIndia

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