Novel computational methods based on Bernoulli operational matrix for time-space fractional advection-dispersion equation

This article investigates the time-space fractional advection-dispersion equation $(TSFADE)$. In this work, an efficient and precise numerical method (Novel Bernoulli Operational Matrix technique) is applied for solving a category of these equations, converting the original problem into a set of algebraic equations that can be solved using numerical methods. The key benefit of this scheme is its ability to transform linear and nonlinear $(PDEs)$ into a set of algebraic equations concerning the expansion coefficients of the solution. The suggested scheme is effectively utilized for the mentioned problem. Sufficient and thorough numerical evaluations are provided to illustrate the precision, applicability, effectiveness, and adaptability of the introduced scheme. To showcase the efficacy and accuracy of this technique, the numerical results from the examples are expressed in a table format to enable comparison with results from other established methods as well as with the precise solutions. It should be noted that the implementation of the current method is regarded as quite simple.