babenko’s attitude based on new sequential ⅁-caputo differential equations via measures of noncompactness

This study examines the existence and uniqueness (eu) of solutions for two nonlinear fractional ides that incorporate a ⅁–based caputo derivative and a ⅁-based riemann–liouville integral. our approach broadens the theoretical framework of the mittag–leffler function, adopts a strategy inspired by babenko, and deploys topological degree theory (tdt) for condensing maps in conjunction with the banach contraction principle.