Mathematical analysis of nonlinear integral boundary value problem of proportional delay implicit fractional differential equations with impulsive conditions
Arshad Ali, Kamal Shah, Thabet Abdeljawad, Ibrahim Mahariq, Mostafa Rashdan
Abstract
Abstract The current study is devoted to deriving some results about existence and stability analysis for a nonlinear problem of implicit fractional differential equations (FODEs) with impulsive and integral boundary conditions. The concerned problem involves proportional type delay term. By using Schaefer’s fixed point theorem and Banach’s contraction principle, the required conditions are developed. Also, different kinds of Ulam stability results are derived by using nonlinear analysis. Providing a pertinent example, we demonstrate our main results.
Topics & Concepts
MathematicsNonlinear systemContraction principleBoundary value problemFixed-point theoremMathematical analysisOrdinary differential equationPartial differential equationDifferential equationApplied mathematicsQuantum mechanicsPhysicsFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisDifferential Equations and Boundary Problems