An accurate RBF–based meshless technique for the inverse multi-term time-fractional integro-differential equation

Abstract

Using the Grünwald difference operator one reduces the inverse boundary value problem of the multi-term time-fractional integro-differential equation (TFIDE) in two dimensions to a system L[u]=F. The backward substitution method (BSM) which is based on the trigonometric basis function (TBF) is developed to a new version and examined for the system. The solution of ill-conditioned TFIDE is expressed in terms of the TBFs on the corrupted boundary data with a small parameter in the noisy data. Finally, the TFIDE model in the complex computational domain is assessed through the methodology with reasonable selective parameters, in addition, high-accuracy solutions and acceptable estimation for the errors are illustrated.