Numerical Solution of Linear/Nonlinear Fractional Order Differential Equations Using Jacobi Operational Matrix
- 7 Downloads
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.
KeywordsFractional 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.
- 4.He, J.H.: Nonlinear oscillation with fractional derivative and its applications. In: International Conference on Vibrating Engineering, Dalian, China, pp. 288–291 (1998)Google Scholar
- 5.He, J.H.: Some applications of nonlinear fractional differential equations and their applications. Bull. Sci. Technol. 15(2), 86–90 (1999)Google Scholar
- 38.Das, S.: Approximate solution of fractional diffusion equation revisited. Int. Rev. Chem. Eng. 4, 501–504 (2012)Google Scholar
- 45.Gorenflo, R., Mainardi, F.: Essentials of fractional calculus. Preprint submitted to MaPhyStocenter (2000)Google Scholar