In this paper Chebyshev wavelet and their properties are employed for deriving Chebyshev wavelet operational matrix of fractional derivatives and a general procedure for forming this matrix is introduced. Then Chebyshev wavelet expansion along with this operational matrix are used for numerical solution of Bagley-Torvik boundary value problems. The error analysis and convergence properties of t...

Regular and singular perturbations of fractional ordinary differential equations (fODEs) are considered. This is likely the first attempt to describe these problems. Similarities and differences between these cases and the analogous ones for classical (integer-order) differential equations are pointed out. Examples, including the celebrated Bagley-Torvik equations are discussed. Asymptotic-nume...

The motion differential equation of hydro-pneumatic suspension is established to describe the vibration characteristics for a certain type construction vehicle. output force was deduced from parameters. Based on multi-phase medium, fractional calculus theory introduced, and its Bagley–Torvik formed. numerical computation by low-pass filter Oustaloup algorithm performed. solution nonlinear obtai...