\frac{k^{-a-1} \left(t^2\right)^{-a/2} e^{-i k \sqrt{t^2}} \left(k^a e^{2 i k
   \sqrt{t^2}} \left(-\frac{1}{2} i t^a \left(t^2\right)^{\frac{a}{2}+\frac{1}{2}}
   \Gamma \left(-\frac{a}{2}\right)+\frac{a t^a \left(t^2\right)^{a/2} \Gamma
   \left(-\frac{a}{2}\right)}{2 k}+O\left(\left(\frac{1}{k}\right)^2\right)\right)+k^a
   \left(\frac{1}{2} i t^a \left(t^2\right)^{\frac{a}{2}+\frac{1}{2}} \Gamma
   \left(-\frac{a}{2}\right)+\frac{a t^a \left(t^2\right)^{a/2} \Gamma
   \left(-\frac{a}{2}\right)}{2
   k}+O\left(\left(\frac{1}{k}\right)^2\right)\right)+\sqrt{\pi } 2^a \sqrt{t^2} t^a
   \Gamma \left(\frac{a}{2}+\frac{1}{2}\right) e^{i k \sqrt{t^2}}\right)}{t \Gamma
   \left(-\frac{a}{2}\right)}