A NOVEL NUMERICAL METHOD FOR SOLVING MODIFIED ATANGANA–BALEANU FRACTIONAL PROBLEMS BASED ON THE OPERATIONAL MATRIX METHOD

A novel numerical method for solving modified Atangana–Baleanu fractional problems based on the operational matrix method is presented in this paper. We modify the operational matrix method so that its coefficients can be found in an iterative, direct manner. This avoids solving a large algebraic system, which would be computationally expensive. Several theoretical results are presented, including the existence and uniqueness of the solution for our problem, as well as uniform convergence and error estimates. Examples are provided to demonstrate the efficiency of our numerical approach. Both numerical and theoretical results show that our modified approach works very efficiently. Several applications are discussed.