*Correspondence: [email protected] Department of Mathematics, Eastern Mediterranean University, Gazimagusa, Turkish Republic of Northern Cyprus Abstract In this paper, we study existence (uniqueness) of solutions for nonlinear fractional differential equations with Katugampola fractional integral conditions. Several fixed point theorems are used for sufficient conditions of existence (u...

In this paper we consider a nonlinear system of differential equations arising in tumour invasion which has been proposed in [1]. The system consists of two PDEs describing the evolution of tumour cells and proteases and an ODE which models the concentration of the extracellular matrix. We prove local existence and uniqueness of solutions in the class of Hölder spaces. The proof of local existe...

holds (but which implies that the space is actually a Menger space). Z̆ikić [2] extended the existence part of their theorem showing that it is enough to consider the case of special sequence tn = 1/ n and that (1) holds for some x = x0 and y = f (x0). The error in her main theorem (and in all consequences) concerns the statement that, under the same conditions, also the uniqueness of fixed poin...

In this paper, we study the existence and uniqueness of solutions to the Cauchy problem for nonautonomous fractional differential equations involving Caputo derivative in Banach spaces. Definition for the solution in the Carathéodory sense and fundamental lemma are introduced. Some sufficient conditions for the existence and uniqueness of solutions are established by means of fractional calculu...

In this paper we use the continuation theorem of coincidence degree theory and analysis techniques. We establish the existence and uniqueness of a T-periodic solution for the third-order delay differential equation with two deviating arguments. A new result on the existence and uniqueness of a periodic solution of this equation is obtained. In addition an example is given to illustrate the main...

This paper investigates the existence and uniqueness of nontrivial solutions to a class of fractional nonlocal multi-point boundary value problems of higher order fractional differential equation, this kind of problems arise from viscoelasticity, electrochemistry control, porous media, electromagnetic and signal processing of wireless communication system. Some sufficient conditions for the exi...

The major goal of this manuscript is to investigate the existence, uniqueness, and stability a q-fractional Langevin differential equation with integral conditions. We demonstrate existence uniqueness solution proposed using Banach contraction principle Schaefer’s fixed-point theorem. also elaborate on different kinds Ulam stability. theoretical outcomes are verified by examples.

Due to a singularity or degeneracy at zero time-step, existence and uniqueness, and accuracy, of variational integrators, cannot be established by straightforward use of the implicit function theorem. We show existence and uniqueness for variational integrators by blowing up the variational principle. The blow-up implies an accuracy one less than is observed in simulations, a deficit that is re...

In this paper, we discuss existence and uniqueness of solutions to nonlinear fractional order ordinary differential equations with boundary conditions in an ordered Banach space. We use the Caputo fractional differential operator and the nonlinearity depends on the fractional derivative of an unknown function. Schauder’s fixed point Theorem is the main tool used here to establish the existence ...

We investigate the following nonlinear equations with p-Laplacian-like operators φ x′ t ′ f x t x′ t g x t e t : some criteria to guarantee the existence and uniqueness of periodic solutions of the above equation are given by using Mawhin’s continuation theorem. Our results are new and extend some recent results due to Liu B. Liu, Existence and uniqueness of periodic solutions for a kind of Lie...