New results on fractional neutral integro-differential systems with state-dependent delay via resolvent operators
Journal Title: Discussiones Mathematicae Differential Inclusions Control and Optimization - Year 2017, Vol 37, Issue 1
Abstract
In this manuscript, we set up sufficient conditions for existence and uniqueness of solutions for fractional neutral integro-differential systems (FNIDS) with state-dependent delay (SDD) in Banach spaces. Our methodology depends on resolvent operators, the Banach contraction principle, the Leray-Schauder nonlinear alternative and Schaefer's fixed point theorem. To obtain our results, our working hypotheses are that the functions determining the equation satisfy certain Lipschitz conditions of local type. An illustration is additionally provided to demonstrate the obtained theories.
Authors and Affiliations
Duraisamy Mallika, Dumitru Baleanu, Selvaraj Suganya, Mani Mallika Arjunan
Keywords
Related Articles
- EP ID EP481569
- DOI 10.7151/dmdico.1194
- Views 66
- Downloads 0
Averaging results for semilinear functional differential equations with infinite delay in a Banach space: a case of non uniqueness of solutions
We aim in this paper to establish averaging results in a case of non uniqueness of the mild solutions for semilinear functional differential equations in a Banach space with infinite delay on an abstract phase space and...
Weakly precompact operators on Cb(X,E) with the strict topology
Let X be a completely regular Hausdorff space, E and F be Banach spaces. Let Cb(X,E) be the space of all E-valued bounded continuous functions on X, equipped with the strict topology β. We study weakly precompact operato...
On some properties of quotients of homogeneous C(K) spaces
We say that an infinite, zero dimensional, compact Hausdorff space K has property (*) if for every nonempty open subset U of K there exists an open and closed subset V of U which is homeomorphic to K. We show that if K i...
Upper and Lower Solutions Method for Partial Hadamard Fractional Integral Equations and Inclusions
In this paper we use the upper and lower solutions method combined with Schauder's fixed point theorem and a fixed point theorem for condensing multivalued maps due to Martelli to investigate the existence of solutions f...
On properties of set-valued integrals driven by martingales and set-valued stochastic equations
In the paper we study properties of stochastic integrals of Aumann type driven by quadratic variation process and set-valued Itô integral with respect to martingale. Next, the existence, uniqueness and convergence proper...