Non-instantaneous impulsive Hilfer–Katugampola fractional stochastic differential equations with fractional Brownian motion and Poisson jumps
A. M. Sayed Ahmed, Hamdy M. Ahmed
Abstract
The existence of solutions of non-instantaneous impulsive Hilfer–Katugampola fractional differential equations of order 1/2<α<1 and parameter 0≤β≤1 with fractional Brownian motion (fBm) and Poisson jumps is investigated in this paper. The required results are obtained based on fractional calculus, stochastic analysis, semigroups, and the fixed point theorem. In the end of the paper, an example is provided to illustrate the applicability of the theoretical results.
Topics & Concepts
Fractional Brownian motionMathematicsFractional calculusPoisson distributionApplied mathematicsMathematical analysisStochastic differential equationGeometric Brownian motionOrder (exchange)Brownian motionDiffusion processStatisticsComputer scienceInnovation diffusionEconomicsFinanceKnowledge managementFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisDifferential Equations and Boundary Problems