Solving a class of Volterra integral equations with M-derivative

In this current article, the well-known Neumann method for solving the time M-fractional Volterra integral equations of the second kind is developed. In the several theorems, existence and uniqueness of the solution and convergence of the proposed approach are also studied. The Neumann method for this class of the time M-fractional Volterra integral equations has been called the M-fractional Neumann method (MFNM). The results obtained demonstrate the efficiency of the proposed method for the time M-fractional Volterra integral equations. Several illustrative numerical examples have presented the ability and adequacy of the MFNM for a class of fractional integral equations.

کلیدواژه ها:

Local M-fractional integral ، M-fractional Volterra integral equations ، M-fractional Neumann method ، Existence and uniqueness of solution ، Theorem of convergence