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Hyperbolic Spline Solutions of Fractional Relaxation-Oscillation Equations and Fractional-Order Boundary Value Problems
Hira Tariq and Maria Iftikhar
Abstract:
In complex viscoelastic media, the two phenomenons stress relaxation and oscillation damping have frequently perceptible history and classical models can’t accurately explained physical behaviors in which path is dependent. Latest research revealed that fractional derivative based models can distinguish such damping and complex relaxation. A hyperbolic spline-based numerical scheme is utilized in this study to obtain solutions of the fractional relaxation-oscillation equations (ROE). Additionally, solutions to fractional boundary value problems (BVPs) using hyperbolic splines are covered. Usually, smooth solution of a differential equation (DE) of fractional order cannot be expected and this constitute a question that how to get attainable order of convergence of numerical methods. The convergence behavior of the used numerical scheme is also examined in detail. To verify the robustness of the proposed approach, several numerical examples are provided that highlight its accuracy and computational efficiency.
Keywords:
Relaxation Oscillation Equation; Fractional Boundary-condition Problem; Hyperbolic Spline-based scheme; Caputo sense Fractional Operators; Numerical error estimation.
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