On Fractional Neutral Integro-differential Systems with State-dependent Delay in Banach Spaces

Issue title: Theory and Applications of Fractional Fourier Transform and its Variants

Guest editors: Yudong Zhang, Xiao-Jun Yang, Carlo Cattani, Zhengchao Dong, Ti-Fei Yuan and Liang-Xiu Han

Article type: Research Article

Authors: Kailasavalli, S.^{a; *} | Suganya, S.^{b; †} | Mallika Arjunan, M.^b

Affiliations: [a] Department of Mathematics, PSNA College of Engineering and Technology, Dindigul-624622, Tamil Nadu, India. [email protected] | [b] Department of Mathematics, C. B. M. College, Kovaipudur, Coimbatore - 641 042, Tamil Nadu, India. [email protected], [email protected]

Note: [*] Also affiliated at: Research Scholar, Research & Development Center, Bharathiar University, Tamil Nadu, India

Note: [†] Department of Mathematics, C. B. M. College, Kovaipudur, Coimbatore - 641 042, Tamil Nadu, India

Abstract: Based on concepts for semigroups, fractional calculus, resolvent operator and Banach contraction principle, this manuscript is principally involved with existence results for fractional neutral integro-differential systems with state-dependent delay in Banach spaces. To acquire the main results, our working concepts are that the functions deciding the equation fulfill certain Lipschitz conditions of local type which is similar to the hypotheses [1]. Finally an examples are additionally offered to exhibit the achieved hypotheses.

Keywords: Fractional order differential equations, state-dependent delay, Banach fixed point theorem, resolvent operators, semigroup theory

DOI: 10.3233/FI-2017-1482

Journal: Fundamenta Informaticae, vol. 151, no. 1-4, pp. 109-133, 2017