Solutions of a class of n-th order ordinary and partial differential equations via fractional calculus

Solutions of the n-th order linear ordinary differential equations (z + b)^lΠ^n-1_k=1(z+a_k)φn + ∑ⁿ_k=1φn-k{C^λ_k{Q(z)}k + C^λ_k-1{G(z)}_k-1} = f (z ≠ -a_k (k = 1,2,...,n - 1) z ≠-b; a_i ≠ a_j ≠ b i f i ≠ j; n > l, l ≥ 2) and the partial differential equations (z + b)^lΠ^n-1_k=1(z + a_k) · ∂ⁿμ/∂zⁿ + ∑^n-1_k=1 ∂^n-kμ/∂z^n-k{C^λ _k{Q(z)}_k + C^λ_k-1{G(z)}_k-1} +αμ(z,t) = M∂²μ/∂t² + N∂μ/∂t (z ≠ -a_k (k= 1,2,...,n-l) z ≠ -b; a_i ≠ a_j ≠ b i f i ≠ j; n > l, l ≥ 2) are discussed.