scholarly journals Newton’s law of cooling with fractional conformable derivative

2018 ◽  
Vol 64 (2) ◽  
pp. 172 ◽  
Author(s):  
Abraham Ortega ◽  
J. Juan Rosales
Keyword(s):  
Fractional Order ◽  
Exponential Function ◽  
Order Parameter ◽  
Convection Coefficient ◽  
Smooth Solutions ◽  
Conformable Derivative ◽  
Stretched Exponential ◽  
New Class ◽  
Newton's Law ◽  
Newton’S Law

The fractional conformable derivative and its properties have been introduced recently. Using this derivative we obtain a new class of smooth solutions for the Newton’s law of cooling in terms of a stretched exponential function depending on the fractional order parameter 0 < γ ≤ 1. In addition, the convection coefficient of fractional order k(γ) can be calculated easily. Also, it is shown, that in the particular case γ = 1 these solutions become the ordi- nary ones.

scholarly journals Conformable derivative applied to experimental Newton's law of cooling

2020 ◽  
Vol 66 (2 Mar-Apr) ◽  
pp. 224
Author(s):  
J. Rosales-García ◽  
J. A. Andrade-Lucio ◽  
O. Shulika
Keyword(s):  
Experimental Data ◽  
Free Parameter ◽  
Conformable Derivative ◽  
Data Set ◽  
Stretched Exponential ◽  
The Real ◽  
Integer Order ◽  
Newton's Law ◽  
Newton’S Law

It has been proved that the integer order dierential equation does notrepresent the real behaviour of nature for the Newton's law of cooling.Then, we solve the Newton's cooling law using the conformable deriva-tive, as result we obtain the Kohlrausch stretched exponential function.Due to the free parameter 0 < 1, we can t this function with thegraph of the experimental data set. It is shown that the experimental datacoincide with those theoretical when = 0:77269 and k = 0:018765.

An Application of Newton’s Law Of Cooling

1974 ◽  
Vol 67 (2) ◽  
pp. 141-142
Author(s):  
James F. Hurley
Keyword(s):  
Exponential Function ◽  
Real World ◽  
Radioactive Decay ◽  
Rich Source ◽  
World Population ◽  
The Real ◽  
Newton's Law ◽  
Newton’S Law ◽  
Introductory Calculus ◽  
The Way

Many introductory calculus texts now include a section devoted to applications of the exponential function. The large variety of commonly encountered phenomena whose processes of growth or decay are exponential affords a rich source of interesting and appealing applications. Students who can easily compute the size a century hence of a world population growing continuously at a rate of 2 percent need little further in the way of convincing that calculus can be useful in the real world of today. Problems involving radioactive decay and growth of investments also strike most students as interesting, dealing as they do with questions that, if not familiar, have at least been heard of by most students.

Study of Kynematics and Dynamics in the Traffic of Rembangan Tourism in the Jember Regency as Learning Resources for Physics Learning in the Senior High School

2018 ◽  
Vol 7 (1) ◽  
Author(s):  
Alfido Fauzy Zakaria ◽  
Bambang Supriadi ◽  
Trapsilo Prihandono
Keyword(s):  
High School ◽  
School Teacher ◽  
High School Teacher ◽  
Senior High School ◽  
Circular Motion ◽  
Rectilinear Motion ◽  
Learning Resources ◽  
Physics Learning ◽  
Newton's Law ◽  
Newton’S Law

One branch of physics is mechanics. Based on interviews to Senior High School teacher in Jember, mechanics is difficult to learn. The eksternals factor this chapter is dificult to learn is learning Resources. The learning Resources are often less contextuall with around the phenomenon of students. The contextuall learning Resources in the Jember Regency is study of kynematics and dynamics in the traffic of Rembangan Tourism. From this experiment, we get data can be used as a learning resources chapter uniform rectilinear motion, decelerated uniform rectilinear motion, accelerated uniform rectilinear motion, Newton’s Law, and circular motion.

Analysis of a New Class of Impulsive Implicit Sequential Fractional Differential Equations

2020 ◽  
Vol 21 (6) ◽  
pp. 571-587 ◽  
Author(s):  
Akbar Zada ◽  
Sartaj Ali ◽  
Tongxing Li
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Fractional Differential Equations ◽  
Sufficient Conditions ◽  
Uniqueness Of Solutions ◽  
Integer Order ◽  
New Class ◽  
Proposed Model ◽  
Fractional Differential ◽  
Sequential Fractional Differential Equations

AbstractIn this paper, we study an implicit sequential fractional order differential equation with non-instantaneous impulses and multi-point boundary conditions. The article comprehensively elaborate four different types of Ulam’s stability in the lights of generalized Diaz Margolis’s fixed point theorem. Moreover, some sufficient conditions are constructed to observe the existence and uniqueness of solutions for the proposed model. The proposed model contains both the integer order and fractional order derivatives. Thus, the exponential function appearers in the solution of the proposed model which will lead researchers to study fractional differential equations with well known methods of integer order differential equations. In the last, few examples are provided to show the applicability of our main results.

scholarly journals The dynamics of a new chaotic system through the Caputo–Fabrizio and Atanagan–Baleanu fractional operators

2019 ◽  
Vol 11 (7) ◽  
pp. 168781401986654 ◽  
Author(s):  
Muhammad Altaf Khan
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Order Parameter ◽  
Numerical Procedure ◽  
Numerical Approach ◽  
Fractional Operators ◽  
Fundamental Properties ◽  
Chaotic Model ◽  
New Chaotic System ◽  
Model Apply

The aim of this article is to analyze the dynamics of the new chaotic system in the sense of two fractional operators, that is, the Caputo–Fabrizio and the Atangana–Baleanu derivatives. Initially, we consider a new chaotic model and present some of the fundamental properties of the model. Then, we apply the Caputo–Fabrizio derivative and implement a numerical procedure to obtain their graphical results. Further, we consider the same model, apply the Atangana–Baleanu operator, and present their analysis. The Atangana–Baleanu model is used further to present a numerical approach for their solutions. We obtain and discuss the graphical results to each operator in details. Furthermore, we give a comparison of both the operators applied on the new chaotic model in the form of various graphical results by considering many values of the fractional-order parameter [Formula: see text]. We show that at the integer case, both the models (in Caputo–Fabrizio sense and the Atangana–Baleanu sense) give the same results.

scholarly journals Non-standard compactifications with mass gaps and Newton's law

1999 ◽  
Vol 1999 (10) ◽  
pp. 013-013 ◽  
Author(s):  
Andreas Brandhuber ◽  
Konstadinos Sfetsos
Keyword(s):  
Newton's Law ◽  
Newton’S Law

Fractional order generalized thermoelastic response in a half space due to a periodically varying heat source

2018 ◽  
Vol 14 (1) ◽  
pp. 2-15 ◽  
Author(s):  
Jitesh Tripathi ◽  
Shrikant Warbhe ◽  
K.C. Deshmukh ◽  
Jyoti Verma
Keyword(s):  
Mathematical Model ◽  
Heat Source ◽  
Laplace Transform ◽  
Half Space ◽  
Fractional Order ◽  
Order Parameter ◽  
Order Theory ◽  
Numerical Inversion ◽  
Content Type ◽  
Copper Material

Purpose The present work is concerned with the solution of a fractional-order thermoelastic problem of a two-dimensional infinite half space under axisymmetric distributions in which lower surface is traction free and subjected to a periodically varying heat source. The thermoelastic displacement, stresses and temperature are determined within the context of fractional-order thermoelastic theory. To observe the variations of displacement, temperature and stress inside the half space, the authors compute the numerical values of the field variables for copper material by utilizing Gaver-Stehfast algorithm for numerical inversion of Laplace transform. The effects of fractional-order parameter on the variations of field variables inside the medium are analyzed graphically. The paper aims to discuss these issues. Design/methodology/approach Integral transform technique and Gaver-Stehfast algorithm are applied to prepare the mathematical model by considering the periodically varying heat source in cylindrical co-ordinates. Findings This paper studies a problem on thermoelastic interactions in an isotropic and homogeneous elastic medium under fractional-order theory of thermoelasticity proposed by Sherief (Ezzat and El-Karamany, 2011b). The analytic solutions are found in Laplace transform domain. Gaver-Stehfast algorithm (Ezzat and El-Karamany, 2011d; Ezzat, 2012; Ezzat, El Karamany, Ezzat, 2012) is used for numerical inversion of the Laplace transform. All the integrals were evaluated using Romberg’s integration technique (El-Karamany et al., 2011) with variable step size. A mathematical model is prepared for copper material and the results are presented graphically with the discussion on the effects of fractional-order parameter. Research limitations/implications Constructed purely on theoretical mathematical model by considering different parameters and the functions. Practical implications The system of equations in this paper may prove to be useful in studying the thermal characteristics of various bodies in real-life engineering problems by considering the time fractional derivative in the field equations. Originality/value In this problem, the authors have used the time fractional-order theory of thermoelasticity to solve the problem for a half space with a periodically varying heat source to control the speed of wave propagation in terms of heat and elastic waves for different conductivity like weak conductivity, moderate conductivity and super conductivity which is a new and novel contribution.

Sign in / Sign up

Export Citation Format

Share Document