Existence and Stability of Solutions for Nonlinear Impulsive Nabla Fractional Boundary Value Problems of Order Less Than One - Jonnalagadda, J. M.; Alzabut, J.; Feckan, M. (Discontinuity, Nonlinearity, and Complexity, 2026)
In this paper, we establish sufficient conditions on existence and uniqueness of solutions for a class of nonlinear impulsive nabla fractional difference equations of order α, 0 < α ≤ 1, associated with non–periodic boundary conditions. The right hand side of the proposed equation may grow linearly, or sublinearly in its second argument. We employ the classical fixed point theorem of Schaefer, and the Nonlinear Alternative to prove the existence and uniqueness of solutions. Further, we study stability of solutions in sense of Ulam–Hyers by the help of generalized Gronwall Inequality. To demonstrate the validity and applicability of the established results, we provide a couple of particular examples.