Comp. Appl. Math. https://doi.org/10.1007/s40314-018-0633-3 Jacobi collocation scheme for variable-order fractional reaction-subdiffusion equation R. M. Hafez 1,2 · Y. H. Youssri 3 Received: 16 February 2018 / Revised: 7 April 2018 / Accepted: 23 April 2018 © SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2018 Abstract We developed a numerical scheme to solve the variable-order fractional linear subdiffusion and nonlinear reaction-subdiffusion equations using the shifted Jacobi collo- cation method. Basically, a time-space collocation approximation for temporal and spatial discretizations is employed efficiently to tackle these equations. The convergence and sta- bility analyses of the suggested basis functions are presented in-depth. The validity and efficiency of the proposed method are investigated and verified through numerical examples. Keywords Fractional subdiffusion equation · Fractional nonlinear reaction-subdiffusion equation · Variable-order fractional equations · Shifted Jacobi polynomials · Convergence analysis Mathematics Subject Classification 34A08 · 33C45 · 65M70 1 Introduction Fractional subdiffusion equations are widely used in many applications to model and shape variable phenomena in biomedical sciences, chemistry and physics. Balakrishnan (1985) studied anomalous diffusion using explicitly solvable models. Giona and Roman (1992) used a fractional diffusion equation to model the transport phenomena in a random media. Gorenflo et al. (2002) generated models of random walk in space and time suitable for simulating random variables using fractional diffusion equations. Kosztolowicz (2008) stud- Communicated by José Tenreiro Machado. B Y. H. Youssri youssri@sci.cu.edu.eg 1 Department of Mathematics, Alwagjh University College, University of Tabuk, Tabuk, Saudi Arabia 2 Department of Basic Science, Institute of Information Technology, Modern Academy, Cairo, Egypt 3 Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt 123