General Solution of Basset Equation With Caputo Generalized Hukuhara Derivative

Armand, A.; Allahviranloo, Tofigh; Gouyandeh, Z.

doi:10.11948/2016010

Cited by 7 publications

(1 citation statement)

References 16 publications

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“…The motion dynamics of an object which is submerged into an incompressible fluid is one of the frequently studied topics in engineering literature. Basset [41] proposed an equation and its solution for a sphere moving in a viscous liquid when the sphere is moving in a straight line under the action of a constant force, such as gravity, and also when the sphere is surrounded by viscous liquid and is set in rotation about a fixed diameter and then left to itself [42]. This equation is named as Basset equation and it is expressed by the following fractional order differential equation…”

Section: Examplementioning

confidence: 99%

Stability analysis of fractional differential equations with unknown parameters

Köksal

2019

NAMC

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In this paper, the stability of fractional differential equations (FDEs) with unknown parameters is studied. FDEs bring many advantages to model the physical systems in nature or man-made systems in industry. In fact, real objects are generally fractional and fractional calculus has gained popularity in modelling physical and engineering systems in the last few decades in parallel to advancement of high speed computers. Using the graphical based D-decomposition method, we investigate the parametric stability analysis of FDEs without complicated mathematical analysis. To achieve this, stability boundaries are obtained firstly, and then the stability region set depending on the unknown parameters is found. The applicability of the presented method is shown considering some benchmark equations which are often used to verify the results of a new method. Simulation examples shown that the method is simple and give reliable stability results.

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Section: Examplementioning

confidence: 99%