We construct a computable Banach space which possesses a Schauder basis, but does not possess any computable Schauder basis.

The Balian–Low Theorem is a strong form of the uncertainty principle for Gabor systems which form orthonormal or Riesz bases for L(R). In this paper we investigate the Balian–Low Theorem in the setting of Schauder bases. We prove that new weak versions of the Balian–Low Theorem hold for Gabor Schauder bases, but we constructively demonstrate that several variants of the BLT can fail for Gabor S...

In this study, the existence and uniqueness of weak solution a coupled diffusion system is presented. Since considered problem nonlinear, first we consider corresponding linearized then use convergence method with Schauder fixed-point theorem to prove underlying in an appropriate Hilbert space. Moreover, computational experiments show that model could be applied image restoration problems.

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.

Using Banach’s contractive principle and the Laray–Schauder fixed point theorem, we study uniqueness existence of solutions to a nonlinear two-term fractional integro-differential equation with boundary condition based on Babenko’s approach Mittag–Leffler function. The current work also corrects major errors in published paper dealing one-term differential equation. Furthermore, provide example...

Introduction/purpose: This paper illustrates the existence of a generic Green's function for boundary value problem arbitrary order that appears in many phenomena heat convection, e.g. atmosphere, oceans, and on Sun's surface. Methods: A fixed point theorem Leray-Schauder form has been used to establish problem. Results: The solution shown an Some practical examples are proposed. Conclusions: n.

In this paper, we investigate the controllability of a class impulsive ψ-Caputo fractional evolution equations Sobolev type in Banach spaces. Sufficient conditions are presented by two new characteristic solution operators, calculus, and Schauder fixed point theorem. Our works generalizations continuations recent results about equations. Finally, an example is given to illustrate effectiveness ...

We study the existence and multiplicity of positive solutions for a system Riemann–Liouville fractional differential equations with sequential derivatives, parameters sign-changing singular nonlinearities, subject to nonlocal coupled boundary conditions which contain Riemann–Stieltjes integrals various derivatives. In proof our main results we use nonlinear alternative Leray–Schauder type Guo–K...

In the present research, we study boundary value problems for fractional integro-differential equations and inclusions involving Hilfer derivative. Existence uniqueness results are obtained by using classical fixed point theorems of Banach, Krasnosel’skiĭ, Leray–Schauder in single-valued case, while Martelli’s theorem, a nonlinear alternative multivalued maps, Covitz–Nadler theorem used inclusi...

This paper is devoted to investigating the existence of solutions for fractional differential equation and inclusion order ??(2,3] with affine periodic boundary value conditions. Applying Leray–Schauder fixed point theorem, established. Furthermore, inclusion, we consider two cases: (i) set-valued function has convex (ii) nonconvex value. The main tools our research are alternative Covita Nadle...