Atangana–Baleanu time-fractional stochastic integro-differential equation
McSylvester Ejighikeme Omaba, Cyril Dennis Enyi
Abstract
We study the Atangana–Baleanu time-fractional stochastic integro-differential equation. Using Banach fixed point theory, we prove existence and uniqueness of mild solution. In addition, upper second moment growth estimate of the mild solution is proved and the result gives a precise exponential growth. We also give some specific examples and illustrate their growth moment bounds with graphs.
Topics & Concepts
MathematicsUniquenessMoment (physics)Differential equationFixed-point theoremMathematical analysisApplied mathematicsIntegro-differential equationBanach spaceExponential functionFixed pointExponential growthFirst-order partial differential equationClassical mechanicsPhysicsFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisDifferential Equations and Numerical Methods