Affiliation:
1. King Fahd University of Petroleum & Minerals, Dhahran, SUADI ARABIA
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 RiemannLiouville 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.
Publisher
World Scientific and Engineering Academy and Society (WSEAS)
Subject
Artificial Intelligence,General Mathematics,Control and Systems Engineering
Reference21 articles.
1. R. P. Agarwal, M. Benchohra, and S. Hamani.A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions. Acta Applicandae Mathematicae, 109(3):973–1033, 2010.
2. R. P. Agarwal, S. K. Ntouyas, B. Ahmad, and M. S. Alhothuali. Existence of solutions for integro-differential equations of fractional order with non local three-point fractional boundary conditions. Advances in Difference Equations, 2013(1):1–9, 2013.
3. A. Aghajani, Y. Jalilian, and J. Trujillo. On the existence of solutions of fractional integro-differential equations.Fractional Calculus and Applied Analysis, 15(1):44–69, 2012.
4. A. M. Ahmad, K. M. Furati, and N.-E. Tatar.Asymptotic power type behavior of solutions toa nonlinear fractional integro-differential equation. Electronic Journal of Differential Equations, 2017(134):1–16, 2017.
5. A. M. Ahmad, K. M. Furati, and N.-E.Tatar. Asymptotic behavior of solutions fora class of fractional integro-differential equations.Mediterranean Journal of Mathematics,15(5):188, 2018.
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献