Abstract
The present study seeks to develop a collocation method focused on an extended cubic B-spline (ECBS) to approximate the time fractional coupled-burgers (TFCB) equation. Numerous branches of engineering and physical sciences are used to model the TFCB equation. They have been utilized to simulate the sedimentation of scale volume concentrations of two different types of particles in fluid mixtures under the influence of gravity with the non-local time. The non-local time is considered in the form of the Caputo-Fabrizio operator (CFO). The space-direction is discretized via the ECBS functions. In addition, the new theoretical study of the stability and the convergence are also provided and compared with the computational values. Three examples are tested numerically in order to check the feasibility and applicability of the methodology. The graphics are also provided to examine the order of convergence numerically.
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