On implicit fractional <i>q</i>‐difference equations: Analysis and stability
Nadjet Laledj, Abdelkrim Salım, Jamal Eddine Lazreg, Saı̈d Abbas, Bashir Ahmad, Mouffak Benchohra
Abstract
This paper deals with some existence and Ulam stability results for some classes of implicit fractional ‐difference equations with and without random effects in Banach spaces and Banach algebras. Our results are provided by applying the fixed point theory (Itoh's random fixed point theorem, the nonlinear alternative of Schaefer's type proved by Dhage, and an other Dhage's random fixed point theorem in Banach algebras). Other results about the extremal solutions and random extremal solutions under Carathéodory and certain monotonicity conditions are proved. In the final section, some illustrative examples are provided.
Topics & Concepts
MathematicsFixed-point theoremMonotonic functionBanach spaceStability (learning theory)Fixed pointNonlinear systemPure mathematicsType (biology)Mathematical analysisApplied mathematicsDiscrete mathematicsMachine learningComputer scienceEcologyQuantum mechanicsPhysicsBiologyNonlinear Differential Equations AnalysisFractional Differential Equations SolutionsFunctional Equations Stability Results