A Multiple Fixed Point Result for θ , ϕ , ψ -Type Contractions in the Partially Ordered s -Distance Spaces with an Application

In this manuscript, the aim is to prove a multiple fixed point (FP) result for partially ordered s -distance spaces under θ , ϕ , ψ -type weak contractive condition. The result will generalize some well-known results in literature such as coupled FP (Guo and Lakshmikantham, 1987), triple fixed point (Berinde and Borcut, 2011), and quadruple FP results (Karapinar, 2011). Moreover, to validate the result, an application for the existence of solution of a system of integral equations is also provided.

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.

On Solvability of the Integro-Differential Equations

In this paper, we study the existence of solution to integro-differential equations in the space of Lebesgue-integrable on un-bounded interval after transformed to nonlinear integral functional equation, the used tool is the fixed point theorem due to Schauder with weak measure of non compactness, due to De-Blasi. In addition, we give an example which satisfies the conditions of our existence theorem.

The ordered implicit relations and related fixed point problems in the cone $ b $-metric spaces

<abstract><p>In this paper, we introduce an ordered implicit relation. We present some examples for the illustration of the ordered implicit relation. We investigate conditions for the existence of the fixed points of an implicit contraction. We obtain some fixed point theorems in the cone $ b $-metric spaces and hence answer a fixed-point problem. We present several examples and consequences to explain the obtained theorems. We solve an homotopy problem and show existence of solution to a Urysohn Integral Equation as applications of the obtained fixed point theorem.</p></abstract>

Analytical and Qualitative Study of Some Families of FODEs via Differential Transform Method

This current work is devoted to develop qualitative theory of existence of solution to some families of fractional order differential equations (FODEs). For this purposes we utilize fixed point theory due to Banach and Schauder. Further using differential transform method (DTM), we also compute analytical or semi-analytical results to the proposed problems. Also by some proper examples we demonstrate the results.

Global Existence of Solution for the Fisher Equation via Faedo–Galerkin’s Method

In this study, we consider the Fisher equation in bounded domains. By Faedo–Galerkin’s method and with a homogeneous Dirichlet conditions, the existence of a global solution is proved.

Existence and controllability of higher-order nonlinear fractional integrodifferential systems via resolvent operator

This work analyzes the existence of solution and approximate controllability for higher order non-linear fractional integro-differential systems with Riemann-Liouville derivatives in Banach spaces. Firstly, the definition of mild solution for the system is derived. Then a set of sufficient conditions for the existence of mild solution and approximate controllability of the system is obtained. The discussions are based on fixed point approach, and the theory of convolution and fractional resolvent. To illustrate the feasibility of developed theory, an example is given.