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Controllability discussion for fractional stochastic Volterra–Fredholm integro-differential systems of order 1 &lt; <i>r</i> &lt; 2

C. Dineshkumar, V. Vijayakumar, R. Udhayakumar, Anurag Shukla, Kottakkaran Sooppy Nisar

2022International Journal of Nonlinear Sciences and Numerical Simulation15 citationsDOI

Abstract

Abstract The main motivation of our conversation is the existence and approximate controllability for fractional stochastic Volterra–Fredholm integro-differential systems having order 1 &lt; r &lt; 2. The primary outcomes are obtained by applying concepts and ideas from fractional calculus, multivalued maps, the theory of cosine family, Martelli and Dhage, and Leray–Schauder fixed point techniques. We begin by emphasizing the existence, and then demonstrate the approximate controllability of the considered system. Additionally, we determine the approximate controllability outcomes for the system with infinite delay. At last, an application is established for drawing the theoretical conclusions of primary outcomes.

Topics & Concepts

ControllabilityMathematicsOrder (exchange)Fractional calculusApplied mathematicsDifferential (mechanical device)Trigonometric functionsPure mathematicsMathematical analysisFinancePhysicsThermodynamicsGeometryEconomicsFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisDifferential Equations and Numerical Methods