Existence, Uniqueness, and Stability of Solutions for Nabla Fractional Difference Equations
Nikolay D. Dimitrov, Jagan Mohan Jonnalagadda
Abstract
In this paper, we study a class of nabla fractional difference equations with multipoint summation boundary conditions. We obtain the exact expression of the corresponding Green’s function and deduce some of its properties. Then, we impose some sufficient conditions in order to ensure existence and uniqueness results. Also, we establish some conditions under which the solution to the considered problem is generalized Ulam–Hyers–Rassias stable. In the end, some examples are included in order to illustrate our main results.
Topics & Concepts
Nabla symbolUniquenessStability (learning theory)MathematicsApplied mathematicsMathematical analysisFractional calculusPhysicsComputer scienceOmegaQuantum mechanicsMachine learningFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisDifferential Equations and Numerical Methods