Global Journal of Researches in Engineering, I: Numerical Methods, Volume 23 Issue 1

A pplication A _ cos (3) = -9,899925 x 10 -1 cos (3) = -9,899925 x 10 -1 k = 0 -> k = 0,25 -> k = 0,50 -> k = 0,75 -> k = 1,00 -> k = 1,25 -> The set point - μ k_1 1 1 10 6 − ⋅ + := SL x k , n , ( ) x n k − Γ n 1 + ( ) ⋅ Γ n k − 1 + ( ) := µ 3 := B1 cos µ 0.00 π 2 ⋅ +     cos µ 0.25 π 2 ⋅ +     cos µ 0.50 π 2 ⋅ +     cos µ 0.75 π 2 ⋅ +     cos µ 1.00 π 2 ⋅ +     cos µ 1.25 π 2 ⋅ +                                     := 1 2 3 4 5 2 − 1.5 − 1 − 0.5 − 0 0.989 − cos x( ) _cos x( ) 3 x 13 14 15 16 17 2 − 1.5 − 1 − 0.5 − 0 0.759 − cos x( ) _cos x( ) 15 x A1 1 µ 0.25 − Γ 1( ) ⋅ Γ 1 0.25 − ( ) µ 0.5 − Γ 1( ) ⋅ Γ 1 0.5 − ( ) µ 0.75 − Γ 1( ) ⋅ Γ 1 0.75 − ( ) µ k_1 − Γ 1( ) ⋅ Γ 1 k_1 − ( ) µ 1.25 − Γ 1( ) ⋅ Γ 1 1.25 − ( ) µ µ 1 0.25 − Γ 2 0.25 − ( ) µ 1 0.5 − Γ 2 0.5 − ( ) µ 1 0.75 − Γ 2 0.75 − ( ) µ 1 1 − Γ 2 1 − ( ) µ 1 1.25 − Γ 2 1.25 − ( ) µ 2 2 µ 2 0.25 − ⋅ Γ 3 0.25 − ( ) 2 µ 2 0.5 − ⋅ Γ 3 0.5 − ( ) 2 µ 2 0.75 − ⋅ Γ 3 0.75 − ( ) 2 µ 2 1 − ⋅ Γ 3 1 − ( ) 2 µ 2 1.25 − ⋅ Γ 3 1.25 − ( ) µ 3 6 µ 3 0.25 − ⋅ Γ 4 0.25 − ( ) 6 µ 3 0.5 − ⋅ Γ 4 0.5 − ( ) 6 µ 3 0.75 − ⋅ Γ 4 0.75 − ( ) 6 µ 3 1 − ⋅ Γ 4 1 − ( ) 6 µ 3 1.25 − ⋅ Γ 4 1.25 − ( ) µ 4 24 µ 4 0.25 − ⋅ Γ 5 0.25 − ( ) 24 µ 4 0.5 − ⋅ Γ 5 0.5 − ( ) 24 µ 4 0.75 − ⋅ Γ 5 0.75 − ( ) 24 µ 4 1 − ⋅ Γ 5 1 − ( ) 24 µ 4 1.25 − ⋅ Γ 5 1.25 − ( ) µ 5 120 µ 5 0.25 − ⋅ Γ 6 0.25 − ( ) 120 µ 5 0.5 − ⋅ Γ 6 0.5 − ( ) 120 µ 5 0.75 − ⋅ Γ 6 0.75 − ( ) 120 µ 5 1 − ⋅ Γ 6 1 − ( ) 120 µ 5 1.25 − ⋅ Γ 6 1.25 − ( )                                 := a A1 1 − B1 ⋅ := _cos x( ) a 0 a 1 x ⋅ + a 2 x 2 ⋅ + a 3 x 3 ⋅ + a 4 x 4 ⋅ + a 5 x 5 ⋅ + := _cos 15( ) 7.596879 − 10 1 − × = cos 15( ) 7.596879 − 10 1 − × = Figure A.1: Decomposition of the function cos (x) into a series _cos(x ) in the vicinity of two different points μ =3 and μ = 15 The system consists of the polynomial cos (x) and its six fractional derivatives ki , with a maximum multiplicity of 1.25. The order of the derivatives of k changes after 0.25. © 2023 Global Journals Global Journal of Researches in Engineering Volume XxXIII Issue I Version I 23 Year 2023 ( ) I Application of Differentialintegral Functions