Some results on the existence of weak periodic solutions for quasilinear parabolic systems with L1 data

The aim of this paper is to prove the existence of weak periodic solution and super solution for M×M reaction diffusion system with L1 data and nonlinearity on the gradient. The existence is proved by the technique of sub and super solution and Schauder fixed point theorem.

On Pentagonal Controlled Fuzzy Metric Spaces with an Application to Dynamic Market Equilibrium

In this manuscript, we coined pentagonal controlled fuzzy metric spaces and fuzzy controlled hexagonal metric space as generalizations of fuzzy triple controlled metric spaces and fuzzy extended hexagonal b-metric spaces. We use a control function in fuzzy controlled hexagonal metric space and introduce five noncomparable control functions in pentagonal controlled fuzzy metric spaces. In the scenario of pentagonal controlled fuzzy metric spaces, we prove the Banach fixed point theorem, which generalizes the Banach fixed point theorem for the aforementioned spaces. An example is offered to support our main point. We also presented an application to dynamic market equilibrium.

Periodic solutions to a generalized Basener-Ross model with time-dependent coefficients

This paper is devoted to studying the existence of at least one periodic solution for a generalized Basener-Ross model with time-dependent coefficients. The discussion is based on the Man\’asevich-Mawhin continuation theorem and fixed point theorem of cone mapping together with some properties of Green’s function.

The Ulam Stability of Fractional Differential Equation with the Caputo-Fabrizio Derivative

The aim of this paper is to establish the Ulam stability of the Caputo-Fabrizio fractional differential equation with integral boundary condition. We also present the existence and uniqueness results of the solution for the Caputo-Fabrizio fractional differential equation by Krasnoselskii’s fixed point theorem and Banach fixed point theorem. Some examples are provided to illustrate our theorems.

Extension of Darbo’s fixed point theorem via shifting distance functions and its application

In this paper, we discuss solvability of infinite system of fractional integral equations (FIE) of mixed type. To achieve this goal, we first use shifting distance function to establish a new generalization of Darbo’s fixed point theorem, and then apply it to the FIEs to establish the existence of solution on tempered sequence space. Finally, we verify our results by considering a suitable example.

Multivalued and random version of Perov fixed point theorem in generalized gauge spaces

In this paper, we present some random fixed point theorems in complete gauge spaces. We establish then a multivalued version of a Perov–Gheorghiu’s fixed point theorem in generalized gauge spaces. Finally, some examples are given to illustrate the results.