 We might think that mathematical precision is what drives the wheels of science and engineering forward. But in reality, approximation plays a huge role, and researchers keep getting better at it. One research team has adapted a method for approximating solutions in traditional calculus to a branch of mathematics known as fractional calculus. Because this more exotic math is already helping researchers create richer models of systems as complex as the economy and the human body, the new method could provide a much welcome to boost to their computational efforts. Many problems in science and engineering, the positioning of satellites in space, the rippling of earthquakes, and even the spread of viruses are tackled using fractional calculus. That's because, compared with traditional calculus, fractional calculus is better equipped to capture the memory-like effects observed in these systems. The resulting equations are highly complex, so there's almost never an exact solution. But getting a close approximation is often good enough. The researchers showed that one way to do this is to first impose a specific set of constraints. Like mathematical blinders, these constraints help narrow the scope of the problem and allow a function to be approximated as a series of byte-size functions. That makes each calculation easier. And because each term, in this so-called fractional Taylor series, is slightly more complex than the last, the estimate gradually draws nearer to the exact function. A handful of terms usually does the trick. The given problem is then converted to a fractional integral equation, and a special matrix, known as an operational matrix, is used to carry out the integration. Finally, a method called co-location is applied to reduce the problem to a system of linear equations, much like those encountered in algebra. The research team showed that this shortcut works well for fractional calculus equations. When compared with other methods for solving fractional equations, the researchers showed that using a fractional Taylor series produces results that are just as accurate and as easy as solving algebraic equations. That could make the technique a vital part of researchers' toolkits. It could also provide a clear mathematical picture of some of today's most intricate problems and help advance the fields of science and engineering.