Nonlinear contraction in bb-suprametric spaces

We introduce the concept of $b$-suprametric spaces and establish a fixed point result for mappings satisfying a nonlinear contraction in such spaces. The obtained result generalizes a fixed point theorem of Czerwik and a recent result of the author.Comment: 8 page

On a new variant of F-contractive mappings with application to fractional differential equations

The present article intends to prove the existence of best proximity points (pairs) using the notion of measure of noncompactness. We introduce generalized classes of cyclic (noncyclic) F-contractive operators, and then derive best proximity point (pair) results in Banach (strictly convex Banach) spaces. This work includes some of the recent results as corollaries. We apply these conclusions to prove the existence of optimum solutions for a system of Hilfer fractionaldifferential equations

System of fractional boundary value problem with p-Laplacian and advanced arguments

In this paper, we discuss the existence and multiplicity of positive solutions for a system of fractional differential equations with boundary condition and advanced arguments. The existence result is proved via Leray–Schauder’s fixed point theorem type in a vector Banach space. Further, by using a new fixed point theorem in order Banach space, we study the multiplicity of positive solutions. Finally, some examples are given to illustrate our resultsThe research of J.J. Nieto has been partially supported by the Agencia Estatal de Investigación (AEI) of Spain under Grant MTM2016-75140-P, co-financed by the European Community fund FEDER, and by Xunta de Galicia under grant ED431C 2019/02S

New general integral transform via Atangana–Baleanu derivatives

Abstract The current paper is about the investigation of a new integral transform introduced recently by Jafari. Specifically, we explore the applicability of this integral transform on Atangana–Baleanu derivative and the associated fractional integral. It is shown that by applying specific conditions on this integral transform, other integral transforms are deduced. We provide examples to reinforce the applicability of this new integral transform

Analysis of the Ebola with a fractional-order model involving the Caputo-Fabrizio derivative

This paper uses a fractional-order epidemic model to describe the transmission dynamics of the Ebola virus. The proposed model uses the fractional-order derivative in Caputo-Fabrizio’s sense. It calculates the time-independent solutions of the proposed model, and the next-generation matrix method is used to calculate the basic reproduction number. It provides the conditions for the existence and uniqueness of solutions to the model. Further, the conditions for generalized Ulam-Hyers-Rassias stability of the proposed model are obtained. Numerical simulations show how the proposed model’s approximate solution varies for integer and fractional orders. They also show the behavior of the Ebola in terms of infections, deceased, and susceptible counts, for various contact rates. To demonstrate efficiency while using less time, CPU times are given in tabular form

Controllability of fractional differential evolution equation of order γ∈(1,2) with nonlocal conditions

This paper investigates the existence of positive mild solutions and controllability for fractional differential evolution equations of order with nonlocal conditions in Banach spaces. Our approach is based on Schauder's fixed point theorem, Krasnoselskii's fixed point theorem, and the Arzelà-Ascoli theorem. Finally, we include an example to verify our theoretical results

Fundamental solutions for semidiscrete evolution equations via Banach algebras

We give representations for solutions of time-fractional differential equations that involve operators on Lebesgue spaces of sequences defined by discrete convolutions involving kernels through the discrete Fourier transform. We consider finite difference operators of first and second orders, which are generators of uniformly continuous semigroups and cosine functions. We present the linear and algebraic structures (in particular, factorization properties) and their norms and spectra in the Lebesgue space of summable sequences. We identify fractional powers of these generators and apply to them the subordination principle. We also give some applications and consequences of our results

Advances in Optimization and Nonlinear Analysis

The present book focuses on that part of calculus of variations, optimization, nonlinear analysis and related applications which combines tools and methods from partial differential equations with geometrical techniques. More precisely, this work is devoted to nonlinear problems coming from different areas, with particular reference to those introducing new techniques capable of solving a wide range of problems. The book is a valuable guide for researchers, engineers and students in the field of mathematics, operations research, optimal control science, artificial intelligence, management science and economics