I was reading an article about using a Laplace Transform on a fractional differential equation and attempted to derieve a formula that was just skipped over to.
The Laplace transform is as follows: saT(s)-s(a-1)T(0)=mT(s)-(mTa/s)
The end result should be T(s)=[(sa-1)/(sa-m)]((T(0)-Ta)+(Ta/s)
However, I have only been able to get to T(s)=[(sa-1)/(sa-m)] (T(0))-[mTa/(s(sa-m))]. I haven't been able to find a way to simplfy the [mTa/(s(sa-m))] section so that I can reach the final equation.
I would be so grateful if someone could let me know how to reach the final equation. If looking at the article is better, it is from equation (17) to (18) on page 4 of the PDF. Thank you so much.