New discussion on approximate controllability results for fractional Sobolev type <scp>Volterra‐Fredholm</scp> integro‐differential systems of order 1 < <i>r</i> < 2
V. Vijayakumar, C. Ravichandran, Kottakkaran Sooppy Nisar, Kishor D. Kucche
Abstract
Abstract In our article, we are primarily concentrating on approximate controllability results for fractional Sobolev type Volterra‐Fredholm integro‐differential inclusions of order 1 < r < 2. By applying the results and ideas belongs to the cosine function of operators, fractional calculus and fixed point approach, the main results are established. Initially, we establish the approximate controllability of the considered fractional system, then continue to examine the system with the concept of nonlocal conditions. In the end, we present an example to demonstrate the theory.
Topics & Concepts
ControllabilityMathematicsSobolev spaceFractional calculusOrder (exchange)Type (biology)Fixed-point theoremTrigonometric functionsDifferential (mechanical device)Mathematical analysisFunction (biology)Applied mathematicsVolterra equationsPure mathematicsNonlinear systemGeometryEcologyEvolutionary biologyAerospace engineeringEconomicsEngineeringBiologyPhysicsQuantum mechanicsFinanceNonlinear Differential Equations AnalysisNumerical methods in engineeringDifferential Equations and Boundary Problems