Abstract We investigate the properties of some recently developed variable-order differential operators involving order transition functions exponential type. Since characterization such is performed in Laplace domain, it necessary to resort accurate numerical methods derive corresponding behaviours time domain. In this regard, we develop a computational procedure solve fractional equations nov...

a computational method for numerical solution of a nonlinear volterra and fredholm integro-differentialequations of fractional order based on chebyshev cardinal functions is introduced. the chebyshev cardinaloperational matrix of fractional derivative is derived and used to transform the main equation to a system ofalgebraic equations. some examples are included to demonstrate the validity and ...