In this paper, we study the existence of integral solutions of fuzzy fractional differential systems with nonlocal conditions under Caputo generalized Hukuhara derivatives. These models are considered in the framework of completegeneralized metric spaces in the sense of Perov. The novel feature of our approach is the combination of the convergentmatrix technique with Schauder fixed point princi...

Some new concepts of generating spaces of quasi-norm family are introduced and their linear topological structures are studied. These spaces are not necessarily locally convex. By virtue of some properties in these spaces, several Schauder-type fixed point theorems are proved, which include the corresponding theorems in locally convex spaces as their special cases. As applications, some new fix...

A basic problem of interest in connection with the study of Schauder frames in Banach spaces is that of characterizing those Schauder frames which can essentially be regarded as Schauder bases. In this paper, we study this problem using the notion of a minimal-associated sequence space and a minimal-associated reconstruction operator for Schauder frames. We prove that a Schauder frame is a near...

‎‎in this paper‎, ‎the existence and uniqueness of positive solutions for a class of nonlinear initial value problem for a finite fractional difference equation obtained by constructing the upper and lower control functions of nonlinear term without any monotone requirement‎ .‎the solutions of fractional difference equation are the size of tumor in model tumor growth described by the gompertz f...

Existence results for semilinear systems of abstract evolution inclusions are established by means of Nadler, Bohnenblust-Karlin and Leray-Schauder fixed point theorems and a new technique for the treatment of systems based on vector-valued metrics and convergent to zero matrices.

In this paper, by using the Schauder fixed point theorem and the Banach contraction principle, we investigate existence and uniqueness of solutions for a class of multi-point boundary value problems of nonlinear fractional q-difference equations. As applications, two examples are presented to show the effectiveness of the obtained results.

Under suitable assumptions we prove, via the Leray-Schauder fixed point theorem, the existence of a solution for quasilinear elliptic boundary value problem in C(Ω̄) ∩ W (Ω), q > N which satisfies in addition the condition, (1+ | x |) 1 2u ∈ C(Ω̄).

In this paper, we discuss nonlinear fractional difference equations with the Caputo like difference operator. Some asymptotic stability results of equations under investigated are obtained by employing Schauder fixed point theorem and discrete Arzela-Ascoli’s theorem. Three examples are also provided to illustrate our main results.

This paper deals with the existence of positive solutions for a boundary value problem involving a nonlinear functional differential equation of fractional order α given by Dαu(t) + f(t, ut) = 0, t ∈ (0, 1), 2 < α ≤ 3, u′(0) = 0, u′(1) = bu′(η), u0 = φ. Our results are based on the nonlinear alternative of Leray-Schauder type and Krasnosel’skii fixed point theorem.