Approximate Iterative Method for Initial Value Problem of Impulsive Fractional Differential Equations with Generalized Proportional Fractional Derivatives

The main aim of the paper is to present an algorithm solve approximately initial value problems for a scalar non-linear fractional differential equation with generalized proportional derivative on finite interval. condition connected one sided Lipschitz right hand side part given equation. An iterative scheme, based appropriately defined mild lower and upper solutions, provided. Two monotone sequences, increasing decreasing ones, are constructed their convergence solutions problem established. In case uniqueness, both limits coincide unique solution problem. approximate method application combined monotone-iterative technique.