Theory and Modern Applications
From: New general integral transform via Atangana–Baleanu derivatives
f(t) | \(T \{ f(t),s \} =\mathcal{F}_{\mathrm{J}}(s)\) |
---|---|
c | \(\frac{\varphi (s)}{\psi (s)}c\), \(c\in \mathbb{R} \) |
t | \(\frac{\varphi (s)}{\psi (s)^{2}}\) |
\(t^{\alpha }\) | \(\frac{\Gamma (\alpha +1)\varphi (s)}{\psi (s)^{\alpha +1}}\), α>0 |
sint | \(\frac{\varphi (s)}{\psi (s)^{2}+1}\) |
cost | \(\frac{\varphi (s)\psi (s)}{\psi (s)^{2}+1}\) |