WSEAS Transactions on Systems and Control
Print ISSN: 1991-8763, E-ISSN: 2224-2856
Volume 15, 2020
The Asymptotic Behavior of Solutions of a Fractional Integro-differential Equation
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Abstract: In this paper, we study the asymptotic behavior of solutions for an initial value problem with a nonlinearfractional integro-differential equation. Most of the existing results in the literature assume the continuity of theinvolved kernel. We consider here a kernel that is not necessarily continuous, namely, the kernel of the Riemann-Liouville fractional integral operator that might be singular. We determine certain sufficient conditions underwhich the solutions, in an appropriate underlying space, behave eventually like power functions. For this purpose,we establish and generalize some well-known integral inequalities with some crucial estimates. Our findings aresupported by examples and numerical calculations.
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Keywords: Fractional differential equation, Caputo fractional derivative, Riemann-Liouville fractional integral,initial value problem, asymptotic behavior, integral inequalities
Pages: 341-348
DOI: 10.37394/23203.2020.15.35