In this work, we investigate the asymptotic stability of zero solution for Caputo-Hadamard fractional dynamic equations on a time scale. We will make use Krasnoselskii fixed point theorem in weighted Banach space to show new results.

Keywords: Analytic semigroup Banach fixed point theorem Caputo derivative Faedo–Galerkin approximations Nonlocal conditions Neutral fractional differential equation a b s t r a c t This paper is concerned with the approximation of the solution for neutral fractional differential equation with nonlocal conditions in an arbitrary separable Hilbert space H. We study an associated integral equation...

We denote by F(T) the set of fixed points of T. Numerous problems in physics, optimization, and economics reduce to find a solution of the equilibrium problem. Some methods have been proposed to solve the equilibrium problem in a Hilbert spaces; see, for instance, Blum and Oettli [1], Combettes and Hirstoaga [2], and Moudafi [3]. Recently, Tada and Takahashi [4, 5] and S. Takahashi and W. Takah...

this paper studies a fractional boundary value problem of nonlineardifferential equations of arbitrary orders. new existence and uniquenessresults are established using banach contraction principle. other existenceresults are obtained using schaefer and krasnoselskii fixed point theorems.in order to clarify our results, some illustrative examples are alsopresented.

This work aims to present a study on the stability analysis of linear and nonlinear incommensurate h-nabla fractional-order difference systems. Several theoretical results are inferred with help using some schemes, such as Z-transform method, Cauchy–Hadamard theorem, Taylor development approach, final-value theorem Banach fixed point theorem. These verified numerically via two illustrative nume...

and Applied Analysis 3 Definition 2.2. For f, g ∈ E the order interval 〈f, g〉 is defined as 17 〈 f, g 〉 { h ∈ E : f ≤ h ≤ g. 2.1 Definition 2.3. A subset E ⊂ Π is called order bounded if E is contained in some order interval. Definition 2.4. A coneK is called normal if there exists a positive constant μ such that f, g ∈ V and θ ≺ f ≺ g implies that ‖f‖ ≤ μ‖g‖. We state the two fixed point resul...

In this paper, we study the existence and uniqueness of solutions for a coupled implicit system involving ψ-Riemann–Liouville fractional derivative with nonlocal conditions. We first transformed problem into an integral then analyzed by means Banach fixed-point theorem Krasnoselskiis theorem. Some known results in literature are extended. Finally, example is given to illustrate our theoretical ...

In this paper, we introduce a general viscosity-type extragradient method for solving the fixed point problem of an asymptotically nonexpansive mapping and variational inclusion with two accretive operators. We obtain strong convergence theorem in setting Banach spaces. terms theorem, establish result (FPP) inequality (VIP) inverse-strongly monotone framework Hilbert Finally, is applied to deal...

in this paper, we introduce intuitionistic fuzzy contraction mappingand prove a fixed point theorem in intuitionistic fuzzy metric spaces.

The aim of this paper is to study a comprehensive dynamics system called fractional fuzzy differential variational inequality, which composed nonlinear equation with Atangana-Baleanu derivative and time-dependent inequality. We explore an existence uniqueness theorem for the under consideration. Our proof based on F-KKM theorem, Banach fixed point principle, theory monotone operators.