The Analytical Solutions of the Stochastic Fractional Kuramoto–Sivashinsky Equation by Using the Riccati Equation Method
Wael W. Mohammed, Abeer M. Albalahi, Sultan Albadrani, Elkhateeb S. Aly, Rabeb Sidaoui, A.E. Matouk
Abstract
In this work, we consider the stochastic fractional-space Kuramoto–Sivashinsky equation using conformable derivative. The Riccati equation method is used to get the analytical solutions to the space-fractional stochastic Kuramoto–Sivashinsky equation. Because this equation has never been examined with space-fractional and multiplicative noise at the same time, we generalize some previous results. Moreover, we display how the multiplicative noise influences on the stability of obtained solutions of the space-fractional stochastic Kuramoto–Sivashinsky equation.
Topics & Concepts
MathematicsRiccati equationMultiplicative functionConformable matrixMultiplicative noiseSpace (punctuation)Mathematical analysisStability (learning theory)Fractional calculusApplied mathematicsPartial differential equationComputer sciencePhysicsOperating systemAnalog signalMachine learningSignal transfer functionComputer hardwareQuantum mechanicsDigital signal processingFractional Differential Equations SolutionsNonlinear Waves and SolitonsNonlinear Dynamics and Pattern Formation