Minimum Energy Problem in the Sense of Caputo for Fractional Neutral Evolution Systems in Banach Spaces

We investigate a class of fractional neutral evolution equations on Banach spaces involving Caputo derivatives. Main results establish conditions for the controllability of the fractional-order system and conditions for existence of a solution to an optimal control problem of minimum energy. The results are proved with the help of fixed-point and semigroup theories.Comment: This is a preprint of a paper whose final and definite form is published Open Access in 'Axioms' at [https://doi.org/10.3390/axioms11080379

Fractional Sobolev spaces with kernel function on compact Riemannian manifolds

In this paper, a new class of Sobolev spaces with kernel function satisfying a Lévy-integrability-type condition on compact Riemannian manifolds is presented. We establish the properties of separability, reflexivity, and completeness. An embedding result is also proved. As an application, we prove the existence of solutions for a nonlocal elliptic problem involving the fractional $p(cdot, cdot)$-Laplacian operator. As one of the main tools, topological degree theory is applied

The Existence and Uniqueness of an Entropy Solution to Unilateral Orlicz Anisotropic Equations in an Unbounded Domain

The purpose of this work is to prove the existence and uniqueness of a class of nonlinear unilateral elliptic problem (P) in an arbitrary domain, managed by a low-order term and non-polynomial growth described by an N-uplet of N-function satisfying the Δ2-condition. The source term is merely integrable

On a new fractional Sobolev space with variable exponent on complete manifolds

We present the theory of a new fractional Sobolev space in complete manifolds with variable exponent. As a result, we investigate some of our new space’s qualitative properties, such as completeness, reflexivity, separability, and density. We also show that continuous and compact embedding results are valid. We apply the conclusions of this study to the variational analysis of a class of fractional ▫$p(z, cdot)$▫-Laplacian problems involving potentials with vanishing behavior at infinity as an application

Homogeneous incompressible Bingham viscoplastic as a limit of bi-viscosity fluids

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