Abbas, MuhammadIqbal, Muhammad KashifBaleanu, DumitruAmin, Muhammad2022-08-292025-09-182022-08-292025-09-182020Amin, Muhammad...et al. (2020). "Numerical Treatment of Time-Fractional Klein–Gordon Equation Using Redefined Extended Cubic B-Spline Functions", Frontiers in Physics, Vol. 8.2296-424Xhttps://doi.org/10.3389/fphy.2020.00288https://hdl.handle.net/20.500.12416/14163Iqbal, Muhammad Kashif/0000-0003-4442-7498; Abbas, Dr. Muhammad/0000-0002-0491-1528In this article we develop a numerical algorithm based on redefined extended cubic B-spline functions to explore the approximate solution of the time-fractional Klein-Gordon equation. The proposed technique employs the finite difference formulation to discretize the Caputo fractional time derivative of order alpha is an element of (1, 2] and uses redefined extended cubic B-spline functions to interpolate the solution curve over a spatial grid. A stability analysis of the scheme is conducted, which confirms that the errors do not amplify during execution of the numerical procedure. The derivation of a uniform convergence result reveals that the scheme isO(h(2)+ Delta t(2-alpha)) accurate. Some computational experiments are carried out to verify the theoretical results. Numerical simulations comparing the proposed method with existing techniques demonstrate that our scheme yields superior outcomes.eninfo:eu-repo/semantics/openAccessRedefined Extended Cubic B-SplineTime Fractional Klein-Gorden EquationCaputo Fractional DerivativeFinite Difference MethodConvergence AnalysisArticle10.3389/fphy.2020.002882-s2.0-85092115826