Are there any integer order differential equations or integral equations that can be solved using fractional calculus? For example, the Abel's Integral (like from the Tautochrone Problem): $$\int_{0}^{h}\dfrac{u(y)}{\sqrt{h-y}}dy=C$$ where $C$ is a constant. Given the Riemann-Liouville Integral: $$I^{\alpha}f(x)=\dfrac{1}{\Gamma(\alpha)}\int f(t)(x-t)^{\alpha-1}dt$$ This problem can easily be solved by representing the integral by the half integral of $u(y)$ and taing the half derivative on both sides.
Are there any other such differential equations that can be solved using fractional calculus?