Existence and controllability of nonlocal mixed<scp>Volterra‐Fredholm</scp>type fractional delay integro‐differential equations of order 1 < <i>r</i> < 2
W. Kavitha Williams, V. Vijayakumar, R. Udhayakumar, Sumati Kumari Panda, Kottakkaran Sooppy Nisar
Abstract
Abstract In our article, we are primarily concentrating on existence and controllability of nonlocal mixed Volterra‐Fredholm type fractional delay integro‐differential equations of order 1 < r < 2. By applying the results and facts belongs to the cosine function of operators, fractional calculus, the measure of noncompactness and fixed point approach, the main results are established. Initially, we focus the existence of mild solution, and later we establish the controllability of the considered fractional system. Finally, we present an example to demonstrate the theory.
Topics & Concepts
ControllabilityMathematicsType (biology)Fractional calculusFixed-point theoremOrder (exchange)Mathematical analysisDifferential equationFunction (biology)Applied mathematicsVolterra equationsTrigonometric functionsNonlinear systemBiologyEcologyEvolutionary biologyFinanceQuantum mechanicsGeometryEconomicsPhysicsNonlinear Differential Equations AnalysisFractional Differential Equations SolutionsDifferential Equations and Boundary Problems