Recently, the dynamical behaviors of a fractional order three species food chain model was studied by Alidousti and Ghahfarokhi (Nonlinear Dynamics, doi: org/10.1007/s11071-018-4663-6, 2018). They proved both the local and global asymptotic stability of all equilibrium points except the interior one. This work extends their work and gives proof of both the local and global stability analysis of the interior equilibrium point. Numerical examples are also provided to substantiate the analytical findings.Research of NB is supported by JU-RUSA 2.0.

Qualitative results for abstract problems are very important in understanding mathematical analysis on which any application is possible. The focus of this paper is twofold: first, we investigate the existence and uniqueness of mild solutions to a generalized Cauchy problem for the nonlinear differential equation with non-local conditions in a Banach space X. This is achievable using some fixed point theorems in infinite dimensional spaces. Secondly, we study the stability results of the system in the sense of Ulam-Hyers-Rassias. Our results improve and generalize most recent related results in the literature.

In this paper we study the existence and uniqueness of μ− pseudo almost automorphic mild solutions for two term fractional order differential equations in a Banach space with μ− pseudo almost automorphic forcing terms. The fractional derivative is understood in the sense of Weyl. We use classical tools to obtain our results.

In this work we are concern with Clifford-valued semi-linear delay differential equations in a Banach space. By using the Banach fixed point theorem, we prove the existence and uniqueness of µ−pseudo almost automorphic solution for Clifford-valued semi-linear delay differential equations.