Review Article

Some Applications of Fractional Calculus in Engineering

Table 1

Fractional-order integrals of several functions.

φ(x),x(I+αφ)(x),x,αC

(x-a)β-1Γ(β)Γ(α+β)(x-a)α+β-1,Re(β)>0
eλxλ-αeλx,Re(λ)>0
{sin(λx)cos(λx)λ-α{sin(λx-απ/2),cos(λx-απ/2),λ>0,Re(α)>1
eλx{sin(γx)cos(γx)eλx(λ2+γ2)α/2{sin(γx-αϕ),ϕ=arctan(γ/λ)cos(γx-αϕ),γ>0,Re(λ)>1