Solvability of a ϱ-Hilfer Fractional Snap Dynamic System on Unbounded Domains
Sabri T. M. Thabet, Miguel José Vivas Cortez, Imed Kédim, Mohammad Esmael Samei, Mohamed Ayari
Abstract
This paper is devoted to studying the ϱ-Hilfer fractional snap dynamic system under the ϱ-Riemann–Liouville fractional integral conditions on unbounded domains [a,∞),a≥0, for the first time. The results concerning the existence and uniqueness, along with the Ulam–Hyers, Ulam–Hyers–Rassias, and semi-Ulam–Hyers–Rassias stabilities, are established in an appropriate special Banach space according to fractional calculus, fixed point theory, and nonlinear analysis. At the end, a numerical example is presented for the interpretation of the main results.
Topics & Concepts
MathematicsUniquenessFractional calculusBanach spaceNonlinear systemFixed-point theoremFixed pointInterpretation (philosophy)Space (punctuation)Applied mathematicsMathematical analysisPure mathematicsComputer scienceQuantum mechanicsProgramming languagePhysicsOperating systemNonlinear Differential Equations AnalysisFunctional Equations Stability ResultsFractional Differential Equations Solutions