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.

In this paper, we consider the second-order three-point boundaryvalue problem u′′(t) + f(t, u, u′, u′′) = 0, 0 ≤ t ≤ 1, u(0) = u(1) = αu(η). Under suitable conditions and using Schauder fixed point theorem, we prove the existence of at least one symmetric positive solution. We also study the existence of positive eigenvalues for this problem. We emphasis the highestorder derivative occurs nonli...

Abstract In the paper, nonlinear systems of mixed-type functional differential equations are analyzed and existence semi-global global solutions is proved. proofs, monotone iterative technique Schauder-Tychonov fixed-point theorem used. addition to proving solutions, estimates their co-ordinates derived as well. Linear variants results considered illustrated by selected examples.

Abstract In the article, we present multiple solutions for a second-order singular Dirichlet boundary value problem that arises when modeling ocean flow of Antarctic Circumpolar Current. The main tools proof are Leray–Schauder nonlinear alternative principle and well-known fixed point theorem in cones.

This work establishes the controllability of nondense fractional neutral delay differential equation under Hille-Yosida condition in Banach space. The outcomes are derived with aid calculus theory, semigroup operator theory and Schauder fixed point theorem. Theoretical results verified through illustration.

This paper studies a coupled system of nonlinear fractional differential equation with three-point boundary conditions. Applying the Schauder fixed point theorem, an existence result is proved for the following system Du (t) = f (t, v (t) , Dv (t)) , t ∈ (0, 1) , Dv (t) = g (t, u (t) , Du (t)) , t ∈ (0, 1) , u (0) = 0, Du (1) = δDu (η) , v (0) = 0, Dv (1) = δDv (η) , where α, β, m, n, η, δ, θ s...

The paper is devoted to studying the solutions of boundary value problem for nonlinear fractional differential equation with Riemann-Liouville type history-state-based variable-order derivative. Using Schauder fixed point theorem and Banach thoerem, we prove existence uniqueness in Hölder space. Lastly, two examples are given show applicability theorems.

this paper presents some results concerning the existence of solutions for a functional integral equation of volterra type in two variables, via measure of noncompactness. two examples are included to illustrate the main result.

Using the Schauder fixed point theorem, we prove existence of impulsive fractional differential equations using Hilfer derivative and nearly sectorial operators in this paper. We’ve gone over two scenarios where related semigroup is compact noncompact for purpose. We also go an example to back up main points.

Random fixed point theorems for condensing 1-set contraction selfmaps are known. But no random fixed point theorem for more general asymptotic 1-set contraction selfmaps is yet available. The purpose of this paper is to prove random fixed point theorems for such maps. 1. Introduction. Random fixed point theorems are stochastic versions of (classical or deterministic) fixed point theorems and ar...