Investigation of the Generalized Proportional Langevin and Sturm–Liouville Fractional Differential Equations via Variable Coefficients and Antiperiodic Boundary Conditions with a Control Theory Application Arising from Complex Networks
Abdelatif Boutiara, Mohammed K. A. Kaabar, Zailan Siri, Mohammad Esmael Samei, Xiao‐Guang Yue
Abstract
This article studies the existence theory of an innovation type of generalized proportional fractional differential equations with the assistance of the technique of Kuratowski measure on noncompactness combined with the fixed-point theorem of Mönch. Also, we use Lebesgue’s dominated convergence theorem and Arzelá–Ascoli fixed point theorem on existence and uniqueness results. An application is also presented by employing two illustrative iks, which enrich our outcomes.
Topics & Concepts
MathematicsFixed-point theoremUniquenessPicard–Lindelöf theoremMathematical analysisComparison theoremConvergence (economics)Boundary value problemDifferential equationVariable (mathematics)Type (biology)Applied mathematicsEcologyEconomicsBiologyEconomic growthFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisStability and Controllability of Differential Equations