Due to the symmetry feature in nature, fractional differential equations precisely measure and describe biological and physical processes. Multiterm time‐fractional order has been introduced to model complex processes in different physical phenomena. This article presents a numerical method based on the cubic B‐spline finite element method for the solution of multiterm time‐fractional differential equations. The temporal fractional part is defined in the Caputo sense while the B‐spline finite element method is employed for space approximation. In addition, the four‐point Gauss−Legendre quadrature is applied to evaluate the source term. The stability of the proposed scheme is discussed by the Von Neumann method, which verifies that the scheme is unconditionally stable. L₂ and L_∞ norms are used to check the efficiency and accuracy of the proposed scheme. Computed results are compared with the exact and available methods in the literature, which show the betterment of the proposed method.

This study aims to find the numerical solution of the Rosenau–Hyman and Fornberg–Whitham equations via the quintic B-spline collocation method. Quintic B-spline, along with finite difference and theta-weighted schemes, is used for the discretization and approximation purposes. The effectiveness and robustness of the procedure is assessed by comparing the computed results with the exact and available results in the literature using absolute and relative error norms. The stability of the proposed scheme is studied using von Neumann stability analysis. Graphical representations are drawn to analyze the behavior of the solution.

Burgers-Huxley model depicts a prototype model of the interaction of convection effect, reaction mechanisms and diffusion transport, used to study the liquid crystal and nerve fibers. This study introduces Galerkin approximation for time-fractional Burgers-Huxley equation (TFBHE). The Caputo derivative is used to evaluate the temporal part using the L ₁ formula. The Galerkin approach employs cubic B-spline as a shape and test function, resulting in a symmetric matrix that is easily convergent. In addition, the three-point quadrature rule is implemented to evaluate the integration of complex function . The Von Neumann analysis is used to discuss stability of the scheme. The performance and robustness of the technique is measured using various error norms The results are compared with the exact solution, demonstrating effectiveness of the proposed method.