Application of the Sumudu Variational Iteration Method with Atangana-Baleanu-Caputo Operator for Solving Fractional-Order Heat-Like Equations with Initial Conditions

Fractional calculus techniques are widely utilized across various engineering disciplines and applied sciences. Among these techniques is the Sumudu Variational Iteration Method (SVIM), which has not yet been tested with the Atangana-Baleanu-Caputo fractional derivative in academic literature. This work aims to explore the application of SVIM for solving fractional-order partial differential equations using the Atangana-Baleanu-Caputo derivative. The method integrates the Sumudu transform with the variational iteration method. To demonstrate the effectiveness and validity of SVIM, we apply it to solve one-dimensional (1-D), two-dimensional (2-D), and three-dimensional (3-D) fractional-order heat-like partial differential equations. The results indicate that SVIM is both convergent and efficient for solving these types of fractional partial differential equations.