Soft,body conformable electronics for thermoregulation enabled by kirigami

The application of thermoelectric devices(TEDs)for personalized thermoregulation is attractive for saving energy while balancing the quality of life.TEDs that directly attach to human skin remarkably minimized the energy wasted for cooling the entire environment.However,facing the extreme dynamic geometry change and strain of human skin,conventional TEDs cannot align with the contour of our bodies for the best thermoregulation effect.Hence,we designed a kirigami-based wearable TED with excellent water vapor permeability,flexibility,and conformability.Numerical analysis and experimental results reveal that our product can withstand various types of large mechanical deformation without circuit rupture.The stated outcome and proposed facile approach not only reinforce the development of wearable TEDs but also offer an innovative opportunity for different electronics that require high conformability.

APPLICATION OF MULTI-DIMENSIONAL OF CONFORMABLE SUMUDU DECOMPOSITION METHOD FOR SOLVING CONFORMABLE SINGULAR FRACTIONAL COUPLED BURGER'S EQUATION

In this article,several theorems of fractional conformable derivatives and triple Sumudu transform are given and proved.Based on these theorems,a new conformable triple Sumudu decomposition method(CTSDM)is intrduced for the solution of singular two-dimensional conformable functional Burger's equation.This method is a combination of the decomposition method(DM)and Conformable triple Sumudu transform.The exact and approximation solutions obtained by using the suggested method in the sense of conformable.Particular examples are given to clarify the possible application of the achieved results and the exact and approximate solution are sketched by using Matlab software.

基于Conformable分数阶导数的灰色Bernoulli模型

为增强灰色Bernoulli模型对各种实际数据序列的适应性,借助分数阶微积分在描述复杂系统中的优势,提出了一种基于Conformable分数阶导数的灰色Bernoulli模型。研究发现,可通过改变结构参数将模型转换为不同的经典灰色预测模型,体现了其统一性。此外,采用粒子群优化算法求解规划模型,获取了模型的最优超参数。最后,用所提模型和5个竞争模型对3个真实案例进行了预测建模,结果表明,所提模型的2项评估指标均优于5个竞争模型,验证了所提模型的有效性和可行性。

一类Conformable分数阶发展包含解集的非空性和紧性

本文利用不动点定理和算子半群理论讨论了Banach空间α∈( 0,1 ]阶Conformable型分数阶发展包含{ Tαx(t)∈Ax(t)+B(t,x(t))u(t)+F(t,x(t)),t∈J:=( 0,b ],x(0)=x0,mild解的存在性以及解集的紧性。This paper utilizes the fixed point theorem and operator semigroup theory to discuss the existence and compactness of the set of mild solutions for the α∈( 0,1 ]-order conformable fractional order evolution inclusion { Tαx(t)∈Ax(t)+B(t,x(t))u(t)+F(t,x(t)),t∈J=[ 0,b ],x(0)=x0..

Exact Solutions and Finite Time Stability of Linear Conformable Fractional Systems with Pure Delay

We study nonhomogeneous systems of linear conformable fractional differential equations with pure delay.By using new conformable delayed matrix functions and the method of variation,we obtain a representation of their solutions.As an application,we derive a finite time stability result using the representation of solutions and a norm estimation of the conformable delayedmatrix functions.The obtained results are new,and they extend and improve some existing ones.Finally,an example is presented to illustrate the validity of our theoretical results.

On Fuzzy Conformable Double Laplace Transform with Applications to Partial Differential Equations

The Laplace transformation is a very important integral transform,and it is extensively used in solving ordinary differential equations,partial differential equations,and several types of integro-differential equations.Our purpose in this study is to introduce the notion of fuzzy double Laplace transform,fuzzy conformable double Laplace transform(FCDLT).We discuss some basic properties of FCDLT.We obtain the solutions of fuzzy partial differential equations(both one-dimensional and two-dimensional cases)through the double Laplace approach.We demonstrate through numerical examples that our proposed method is very successful and convenient for resolving partial differential equations.

Conformable分数阶微分方程三点共振边值问题解的存在性

考虑分数阶微分方程共振边值问题,通过定义合适的Banach空间、范数及算子,利用Mawhin重合度理论,证明Conformable型分数阶微分方程三点共振边值问题解的存在性,并得到了其解存在的一个充分条件.

基于Conformable分数阶导数的COVID-19模型及其数值解

为掌握新冠疫情传播规律、预测其发展趋势以及提供相应的防控依据,找到合适的COVID-19传染病动力学模型,采用SEIRV仓室模型,结合Conformable分数阶导数建立传染病动力学模型。利用数值方法来离散Conformable分数阶导数微分方程,求其数值解。对武汉市2020年1月23号到2020年2月11号的确诊数据进行数值仿真。考虑武汉市政府在2020年2月12号对疫情数据进行了修订,新增数据将近14 000人。通过对SEIRV模型的阶数值进行修正,再对修订后的数据进行仿真。两次仿真结果与公布数据基本吻合。结果表明,相比于传统的整数阶模型,分数阶模型可以对修正后的数据进行仿真。这体现了分数阶传染病动力学模型的优势,并且能对COVID-19模型的预测提供一定的参考价值。

Variational Calculus With Conformable Fractional Derivatives

Invariant conditions for conformable fractional problems of the calculus of variations under the presence of external forces in the dynamics are studied. Depending on the type of transformations considered, different necessary conditions of invariance are obtained. As particular cases, we prove fractional versions of Noether's symmetry theorem. Invariant conditions for fractional optimal control problems, using the Hamiltonian formalism, are also investigated. As an example of potential application in Physics, we show that with conformable derivatives it is possible to formulate an Action Principle for particles under frictional forces that is far simpler than the one obtained with classical fractional derivatives.

Non-Noether symmetries of Hamiltonian systems with conformable fractional derivatives

In this paper, we present the fractional Hamilton＇s canonical equations and the fractional non-Noether symmetry of Hamilton systems by the conformable fractional derivative. First/y, the exchanging relationship between isochronous variation and fractional derivatives, and the fractional Hamilton principle of the system under this fractional derivative are proposed. Secondly, the fractional Hamilton＇s canonical equations of Hamilton systems based on the Hamilton principle are established. Thirdly, the fractional non-Noether symmetries, non-Noether theorem and non-Noether conserved quantities for the Hamilton systems with the conformable fractional derivatives are obtained. Finally, an example is given to illustrate the results.

Exact solutions of stochastic fractional Korteweg de–Vries equation with conformable derivatives

We deal with the Wick-type stochastic fractional Korteweg de–Vries(KdV) equation with conformable derivatives.With the aid of the Exp-function method, white noise theory, and Hermite transform, we produce a novel set of exact soliton and periodic wave solutions to the fractional KdV equation with conformable derivatives. With the help of inverse Hermite transform, we get stochastic soliton and periodic wave solutions of the Wick-type stochastic fractional KdV equation with conformable derivatives. Eventually, by an application example, we show how the stochastic solutions can be given as Brownian motion functional solutions.

On Nonlinear Conformable Fractional Order Dynamical System via Differential Transform Method

This article studies a nonlinear fractional order Lotka-Volterra prey-predator type dynamical system.For the proposed study,we consider the model under the conformable fractional order derivative(CFOD).We investigate the mentioned dynamical system for the existence and uniqueness of at least one solution.Indeed,Schauder and Banach fixed point theorems are utilized to prove our claim.Further,an algorithm for the approximate analytical solution to the proposed problem has been established.In this regard,the conformable fractional differential transform(CFDT)technique is used to compute the required results in the form of a series.Using Matlab-16,we simulate the series solution to illustrate our results graphically.Finally,a comparison of our solution to that obtained for the Caputo fractional order derivative via the perturbation method is given.

On the Nonlinear Neutral Conformable Fractional Integral-Differential Equation

In this paper, we investigate the nonlinear neutral fractional integral-differential equation involving conformable fractional derivative and integral. First of all, we give the form of the solution by lemma. Furthermore, existence results for the solution and sufficient conditions for uniqueness solution are given by the Leray-Schauder nonlinear alternative and Banach contraction mapping principle. Finally, an example is provided to show the application of results.

Existence of Solutions for Fractional Differential Equations with Conformable Fractional Differential Derivatives

A class of nonlinear fractional differential equations with conformable fractional differential derivatives is studied. Firstly, Green's function and its properties are given. Secondly, some new existence and multiplicity conditions of positive solutions are obtained by the use of Leggett-Williams fixed-point theorems on cone.

A different approach for conformable fractional biochemical reaction–diffusion models

This paper attempts to shed light on three biochemical reaction-diffusion models:conformable fractional Brusselator,conformable fractional Schnakenberg,and conformable fractional Gray-Scott.This is done using conformable residual power series(hence-form,CRPS)technique which has indeed,proved to be a useful tool for generating the solution.Interestingly,CRPS is an effective method of solving nonlinear fractional differential equations with greater accuracy and ease.

Conformable fractional heat equation with fractional translation symmetry in both time and space

We investigate the fractional heat equation with fractional translation in both time and position with different fractional orders.As examples,we consider a rod and anα-disk with an initial constant temperature and discuss their cooling processes in the examined formalism.

Exact solutions of conformable time fractional Zoomeron equation via IBSEFM

The nonlinear conformable time-fractional Zoomeron equation is an important mod-el to describe the evolution of a single scalar field.In this paper,new exact solutions of con-formable time-fractional Zoomeron equation are constructed using the Improved Bernoulli Sub-Equation Function Method(IBSEFM).According to the parameters,3D and 2D figures of the solutions are plotted by the aid of Mathematics software.The results show that IBSEFM is an efficient mathematical tool to solve nonlinear conformable time-fractional equations arising in mathematical physics and nonlinear optics.

SBOOSP for Massive Devices in 5G WSNs Using Conformable Chaotic Maps

The commercialization of the fifth-generation(5G)wireless network has begun.Massive devices are being integrated into 5G-enabled wireless sensor networks(5GWSNs)to deliver a variety of valuable services to network users.However,there are rising fears that 5GWSNs will expose sensitive user data to new security vulnerabilities.For secure end-to-end communication,key agreement and user authentication have been proposed.However,when billions of massive devices are networked to collect and analyze complex user data,more stringent security approaches are required.Data integrity,nonrepudiation,and authentication necessitate special-purpose subtree-based signature mechanisms that are pretty difficult to create in practice.To address this issue,this work provides an efficient,provably secure,lightweight subtreebased online/offline signature procedure(SBOOSP)and its aggregation(Agg-SBOOSP)for massive devices in 5G WSNs using conformable chaotic maps.The SBOOSP enables multi-time offline storage access while reducing processing time.As a result,the signer can utilize the pre-stored offline information in polynomial time.This feature distinguishes our presented SBOOSP from previous online/offline-signing procedures that only allow for one signature.Furthermore,the new procedure supports a secret key during the pre-registration process,but no secret key is necessary during the offline stage.The suggested SBOOSP is secure in the logic of unforgeability on the chosen message attack in the random oracle.Additionally,SBOOSP and Agg-SBOOSP had the lowest computing costs compared to other contending schemes.Overall,the suggested SBOOSP outperforms several preliminary security schemes in terms of performance and computational overhead.

一类具有Conformable导数的随机泛函微分方程

本文利用轨道Riemann-Stieltjes积分理论建立了由Hurst指数为H>1/2的分数布朗运动扰动的带Conformable导数的分数阶随机泛函微分方程解的存在唯一性.

On Conformable Delta Fractional Derivative on Time Scales

In this paper, we introduce and investigate the concept of conformable delta fractional derivative on time scales. By using the theory of time scales, we obtain some basic properties of the conformable delta fractional derivative. Our results extend and improve both the results in [9] and the usual delta derivative.