In this study, we examine the existence and Hyers–Ulam stability of a coupled system generalized Liouville–Caputo fractional order differential equations with integral boundary conditions connection to Katugampola integrals. first third theorems, Leray–Schauder alternative Krasnoselskii’s fixed point theorem are used demonstrate solution. The Banach theorem’s concept contraction mapping is in s...

In this paper, we study the existence of solutions for fractional differential equations with Caputo-Hadamard derivative order 2 (1, 2]. The uniqueness result is proved via Banach’s contraction mapping principle and results are established by using Schauder’s fixed point theorem. Furthermore, Ulam-Hyers Ulam-Hyers-Rassias stability proposed equation employed. Some examples given to illustrate r...

A generalization of the classical Leray-Schauder fixed point theorem, based on the infinitedimensional Borsuk-Ulam type antipode construction, is proposed. Two completely different proofs based on the projection operator approach and on a weak version of the well known Krein-Milman theorem are presented. MIRAMARE – TRIESTE May 2007 [email protected]; [email protected]

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...

Winding numbers are fundamental objects arising in algebraic topology, with many applications in non-constructive complex analysis. We present a formalization in Coq of the winding numbers and their main properties. As an application of this development, we also give non-constructive proofs of the following theorems: the Fundamental Theorem of Algebra, the 2-dimensional Brouwer Fixed-Point theo...

The stability problem of functional equations originated from a question of Ulam 1 concerning the stability of group homomorphisms. Hyers 2 gave a first affirmative partial answer to the question of Ulam for Banach spaces. Hyers’ Theorem was generalized by Aoki 3 for additive mappings and by Th. M. Rassias 4 for linear mappings by considering an unbounded Cauchy difference. The paper of Th. M. ...