In this paper, we discuss the existence and uniqueness of points of coincidence and common fixed points for a pair of graph preserving mappings in parametric $N_b$-metric spaces. As some consequences of this study, we obtain several important results in parametric $b$-metric spaces, parametric $S$-metric spaces and parametric $A$-metric spaces. Finally, we provide some illustrative examples to ...

‎The present paper is devoted to the existence and uniqueness result of the fractional evolution equation $D^{q}_c u(t)=g(t,u(t))=Au(t)+f(t)$‎ ‎for the real $qin (0,1)$ with the initial value $u(0)=u_{0}intilde{R}$‎, ‎where $tilde{R}$ is the set of all generalized real numbers and $A$ is an operator defined from $mathcal G$ into itself‎. Here the Caputo fractional derivative $D^{q}_c$ is used i...

The present study aims at indicating the existence and uniqueness result of system in extended colombeau algebra. The Caputo fractional derivative is used for solving the system of ODEs. In addition, Riesz fractional derivative of  Colombeau generalized algebra is considered. The purpose of introducing Riesz fractional derivative is regularizing it in Colombeau sense. We also give a solution to...

This paper considers the existence, uniqueness and non-existence of solution for a quasi-linear fractional boundary value problems with sign-changing Green’s function. Under certain growth conditions on the nonlinear term, we employ the Leray-Schauder alternative fixed point theorem to obtain an existence result of nontrivial solution and use the Banach contraction mapping principle to obtain a...

The purpose of this paper is to study the fuzzy fractional differentialequations. We prove that fuzzy fractional differential equation isequivalent to the fuzzy integral equation and then using this equivalenceexistence and uniqueness result is establish. Fuzzy derivative is considerin the Goetschel-Voxman sense and fractional derivative is consider in theRiemann Liouville sense. At the end, we...

FOLLOING OUR PREVIOS PROJECT [1], WE ARE GOING TO PROVE THE EXISTENCE AND UNIQUENESS OF THE SOLUTION OF THE SPECTRAL PROBLEM IN THIS PROJECT.FIRST,WE HAVE PROVEN THE UNIQUENESS OF THE SOLUTION THEN TO PROVE THE EXISTRNCE WE CONSTENSS OF THE ADJOINT PROBLEM CORRESPONDING TO THIS SPECTRAL PROBLEM NEXT THE UNIQUESS OF THE ADJOINT PROBLEM IS THE EXISTENCE OF THE MAIN PROBLEM AS DISCUSSED BY[2] AND ...