In this article, we discuss the existence and uniqueness of solutions for a new class coupled system sequential fractional differential equations involving ? -Hilfer derivatives, supplemented with multipoint boundary conditions. We make use Banach’s fixed point theorem to obtain result Leray-Schauder alternative result. ...

We study a coupled system of implicit differential equations with fractional-order boundary conditions and the Riemann–Liouville derivative. The existence, uniqueness, at least one solution are established by applying Banach contraction Leray–Schauder fixed point theorem. Furthermore, Hyers–Ulam type stabilities discussed. An example is presented to illustrate our main result. suggested general...

In this paper, assuming a natural sequentially compact conditionwe establish new fixed point theorems for Urysohn type maps between Fréchet spaces. In Section 2 we present new LeraySchauder alternatives, Krasnoselskii and Lefschetz fixed point theory for admissible type maps. The proofs rely on fixed point theory in Banach spaces and viewing a Fréchet space as the projective limit of a sequence...

Let X and Y be Banach spaces, G an open subset of X. If we denote the closure of G by cl(G), let ƒ be a mapping of cl(G) into Y. For X~ Y and ƒ a compact mapping, Leray and Schauder [9] gave a definition of topological degree for mappings of the form ƒ —ƒ on the open set G over a point a of X whenever (I—f)"^) is a compact subset of G. The Leray-Schauder degree for compact displacements is the ...

The current paper intends to report the existence and uniqueness of positive solutions for nonlinear pantograph Caputo–Hadamard fractional differential equations. As part a procedure, we transform specified equation into an equivalent integral equation. We show that this has solution by utilising Schauder fixed point theorem (SFPT) upper lower method. Another method proving singular is Banach (...

This paper is concerned with the existence of solutions for a new boundary value problem nonlinear coupled (k,?)–Hilfer fractional differential equations subject to (k,?)–Riemann–Liouville integral conditions. We prove two results by applying Leray–Schauder alternative, and Krasnosel’ski?’s fixed-point theorem under different criteria, while third result, concerning uniqueness given problem, re...

In this article, we present a two-point boundary value problem with separated conditions for finite nabla fractional difference equation. First, construct an associated Green’s function as series of functions the help spectral theory, and obtain some its properties. Under suitable on nonlinear part equation, deduce two existence results considered by means Leray–Schauder fixed point theorems. W...

First of all, in this paper we obtain a perturbed version the geometric series theorem, which allows us to present an iterative numerical method approximate fixed point contractive affine operator. This result requires some approximations that using projections associated with certain Schauder bases. Next, algorithm is designed solution Fredholm’s linear integral equation, and illustrate behavi...

The purpose of this article is to discuss the existence, uniqueness, and Ulam–Hyers stability solutions a coupled system fractional differential equations with Erdélyi–Kober Riemann–Liouville integral boundary conditions. Banach fixed point theorem used prove uniqueness solutions, while Leray–Schauder alternative existence solutions. Furthermore, we conclude that solution discussed problem Hyer...