An analysis of solutions to fractional neutral differential equations with delay. (English) Zbl 1468.34105
Summary: This paper discusses some properties of solutions to fractional neutral delay differential equations. By combining a new weighted norm, the Banach fixed point theorem and an elegant technique for extending solutions, results on existence, uniqueness, and growth rate of global solutions under a mild Lipschitz continuous condition of the vector field are first established. Be means of the Laplace transform the solution of some delay fractional neutral differential equations are derived in terms of three-parameter Mittag-Leffler functions; their stability properties are hence studied by using use Rouché’s theorem to describe the position of poles of the characteristic polynomials and the final value theorem to detect the asymptotic behavior. By means of numerical simulations the theoretical findings on the asymptotic behavior are verified.
MSC:
| 34K37 | Functional-differential equations with fractional derivatives |
| 34K40 | Neutral functional-differential equations |
| 34K20 | Stability theory of functional-differential equations |
| 47N20 | Applications of operator theory to differential and integral equations |
| 34K25 | Asymptotic theory of functional-differential equations |
Keywords:
fractional derivative; fractional neutral differential equation with delay; existence and uniqueness of solutions; exponential boundedness; stability; numerical simulationReferences:
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