Abel 1826 tautochrone problem: ∫_0^x (x-t)^{-α} f(t) dt = g(x) inverted via fractional-integration. Solution f(x) = (sin πα/π) d/dx ∫_0^x (x-t)^{α-1} g(t) dt. Foundational singular-kernel integral equation.
Abel 1826 tautochrone problem: ∫_0^x (x-t)^{-α} f(t) dt = g(x) inverted via fractional-integration. Solution f(x) = (sin πα/π) d/dx ∫_0^x (x-t)^{α-1} g(t) dt. Foundational singular-kernel integral equation.