Reconstruction of a space-dependent source in the inexact order time-fractional diffusion equation

•A general modified quasi-boundary value regularization method is proposed to solve the inverse source problem of the time-fractional diffusion equation with inexact order.•The proposed technique is extendable to solve the continuous spectrum of the inverse and ill-posed parabolic partial differential equations.•Order optimal convergence rates for the worst case error of the method are derived under the usual source condition by using an a-priori and an a-posteriori regularization parameter choice rules, respectively.•Several numerical examples are provided to illustrate the effectiveness of the proposed method.