in this article, we apply two new fixed point theorems to investigate the existence of mild solutions for a nonlocal fractional cauchy problem with an integral initial condition in banach spaces.

*Correspondence: [email protected] Department of Mathematics, National Kaohsiung Normal University, Kaohsiung, 824, Taiwan Abstract In this paper, we first establish some new existence theorems of coincidence points and common fixed points forMT -functions. By applying our results, we obtain some generalizations of Mizoguchi-Takahashi’s fixed point theorem, Nadler’s fixed point theorem a...

The theory of modular space was initiated by Nakano [1] in connection with the theory of order spaces and was redefined and generalized byMusielak and Orlicz [2]. By defining a norm, particular Banach spaces of functions can be considered. Metric fixed theory for these Banach spaces of functions has been widely studied (see [3]). Another direction is based on considering and abstractly given fu...

In this paper we prove an analogue of Banach and Kannan fixed point theorems by generalizing the Lipschitz constat $k$, in generalized Lipschitz mapping on cone metric space over Banach algebra, which are answers for the open problems proposed by Sastry et al, [K. P. R. Sastry, G. A. Naidu, T. Bakeshie, Fixed point theorems in cone metric spaces with Banach algebra cones, Int. J. of Math. Sci. ...

In 2007, Huang and Zhang in 1 introduced cone metric space by substituting an ordered Banach space for the real numbers and proved some fixed point theorems in this space. Many authors study this subject and many fixed point theorems are proved; see 2–5 . In this paper, the concept of integral in this space is introduced and a fixed point theorem is proved. In order to do this, we recall some d...

We develop the theory of hybrid fractional differential equations with the complex order $thetain mathbb{C}$, $theta=m+ialpha$, $0<mleq 1$, $alphain mathbb{R}$, in Caputo sense. Using Dhage's type fixed point theorem for the product of abstract nonlinear operators in Banach algebra; one of the operators is $mathfrak{D}$- Lipschitzian and the other one is completely continuous, we prove the exis...

In this paper, we study the existence of solutions for fractional evolution equations with nonlocalconditions. These results are obtained using Banach contraction xed point theorem. Other resultsare also presented using Krasnoselskii theorem.

  In this paper, an existence result for a class of infinite systems of functional-integral equations in the Banach sequence space $c_{0}$ is established via the well-known Schauder fixed-point theorem together with a criterion of compactness in the space $c_{0}$. Furthermore, we include some remarks to show the vastity of the class of infinite systems which can be covered by our result. The a...

Sufficient conditions for controllability of semilinear integrodifferential systems in a Banach space are established. The results are obtained by using the Schaefer fixed-point theorem.