In this paper, we study the solution of the fractional nonlinear Ginzburg-Landau(FNGL) equation with weak initial data in the weighted Lebesgue spaces. The existence of a solution to this equation is proved by the contraction-mapping principle.

Abstract In this research we introduce and study a new coupled system of three fractional differential equations supplemented with nonlocal multi-point boundary conditions. Existence uniqueness results are established by using the Leray–Schauder alternative Banach’s contraction mapping principle. Illustrative examples also presented.

The well known contraction mapping principle or Banach’s fixed point theorem asserts: The method for successive substitutions converges only linearly to a fixed point of an operator equation in a Banach space setting [5], [7]. In practice, if Newton’s method is used one ignores the additional information about the contraction mapping information. Werner in [9] provided a local analysis for a Ne...

In this paper, we obtain the existence of unique solution anti-periodic type (anti-symmetry) integral multi-point boundary conditions for sequential fractional differential equations. We apply Banach contraction mapping principle to get desired results. Our results specialize and extend some existing

Let (X , d) be a complete metric space, m ∈ N \ {0}, and γ ∈ R with 0 ≤ γ < 1. A g-contraction is a mapping T : X −→ X such that for all x, y ∈ X there is an i ∈ [1,m] with d(T ix,T iy) <R γid(x, y). The generalized Banach contractions principle states that each g-contraction has a fixed point. We show that this principle is a consequence of Ramsey’s theorem for pairs over, roughly, RCA0 + Σ2-I...

Abstract In this paper, a class of nonlinear ? -Hilfer fractional integrodifferential coupled systems on bounded domain is investigated. The existence and uniqueness results for the are proved based contraction mapping principle. Moreover, Ulam–Hyers–Rassias, Ulam–Hyers, semi-Ulam–Hyers–Rassias stabilities to initial value problem obtained.

Abstract We study a free-boundary fluid–structure interaction problem with growth, which arises from the plaque formation in blood vessels. The fluid is described by incompressible Navier–Stokes equations, while structure considered as viscoelastic neo-Hookean material. Moreover, growth due to biochemical process taken into account. Applying maximal regularity theory linearization of along defo...