scholarly journals Simpson’s Integral Inequalities for Twice Differentiable Convex Functions

2020 ◽  
Vol 2020 ◽  
pp. 1-15 ◽  
Author(s):  
Miguel Vivas-Cortez ◽  
Thabet Abdeljawad ◽  
Pshtiwan Othman Mohammed ◽  
Yenny Rangel-Oliveros
Keyword(s):  
Mathematical Model ◽  
Fractional Calculus ◽  
Mathematical Analysis ◽  
Integral Inequality ◽  
Special Functions ◽  
Quasiconvex Functions ◽  
Second Derivative ◽  
Integral Type ◽  
Research Article ◽  
New Inequalities

Integral inequality is an interesting mathematical model due to its wide and significant applications in mathematical analysis and fractional calculus. In the present research article, we obtain new inequalities of Simpson’s integral type based on the φ-convex and φ-quasiconvex functions in the second derivative sense. In the last sections, some applications on special functions are provided and shown via two figures to demonstrate the explanation of the readers.

scholarly journals General Raina fractional integral inequalities on coordinates of convex functions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Dumitru Baleanu ◽  
Artion Kashuri ◽  
Pshtiwan Othman Mohammed ◽  
Badreddine Meftah
Keyword(s):  
Mathematical Model ◽  
Fractional Calculus ◽  
Convex Function ◽  
Mathematical Analysis ◽  
Integral Inequality ◽  
Convex Functions ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Differentiable Functions ◽  
Special Cases

AbstractIntegral inequality is an interesting mathematical model due to its wide and significant applications in mathematical analysis and fractional calculus. In this study, authors have established some generalized Raina fractional integral inequalities using an $(l_{1},h_{1})$ ( l 1 , h 1 ) -$(l_{2},h_{2})$ ( l 2 , h 2 ) -convex function on coordinates. Also, we obtain an integral identity for partial differentiable functions. As an effect of this result, two interesting integral inequalities for the $(l_{1},h_{1})$ ( l 1 , h 1 ) -$(l_{2},h_{2})$ ( l 2 , h 2 ) -convex function on coordinates are given. Finally, we can say that our findings recapture some recent results as special cases.

scholarly journals Hermite–Hadamard Type Inequalities Involving k-Fractional Operator for (h¯,m)-Convex Functions

Symmetry ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1686 ◽  
Author(s):  
Soubhagya Kumar Sahoo ◽  
Hijaz Ahmad ◽  
Muhammad Tariq ◽  
Bibhakar Kodamasingh ◽  
Hassen Aydi ◽  
...  
Keyword(s):  
Integral Inequality ◽  
Convex Functions ◽  
Fractional Integral ◽  
Special Functions ◽  
Fractional Operator ◽  
Hadamard’S Inequality ◽  
Integral Equality ◽  
Symmetric Property ◽  
New Inequalities

The principal motivation of this paper is to establish a new integral equality related to k-Riemann Liouville fractional operator. Employing this equality, we present several new inequalities for twice differentiable convex functions that are associated with Hermite–Hadamard integral inequality. Additionally, some novel cases of the established results for different kinds of convex functions are derived. This fractional integral sums up Riemann–Liouville and Hermite–Hadamard’s inequality, which have a symmetric property. Scientific inequalities of this nature and, particularly, the methods included have applications in different fields in which symmetry plays a notable role. Finally, applications of q-digamma and q-polygamma special functions are presented.

scholarly journals Mathematical model of survival of fractional calculus, critics and their impact: How singular is our world?

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Abdon Atangana
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Lyapunov Function ◽  
Fractional Calculus ◽  
Reproductive Number ◽  
Second Derivative ◽  
Suggested Model ◽  
Stochastic Version ◽  
The Past ◽  
Elementary Analysis

AbstractFractional calculus as was predicted by Leibniz to be a paradox, has nowadays evolved to become a centre of interest for many researchers from various backgrounds. As a result, multiple innovative ideas had emerged, which caused significant divisions regarding fractional calculus in the past three years. Therefore, this work is aimed at developing a mathematical model that could be used to depict the survival of fractional calculus. Six classes are herein considered to construct a mathematical model with six ordinary differential equations. All elementary analysis have been performed. Additionally, a new analysis including strength number that accounts for the accelerative information of nonlinear and linear parts of a given epidemiological model is introduced. An analysis of the second derivative of the Lyapunov function as well as an analysis of the second derivative of each class is applied to assess how a wave could be detected. It is strongly believed that this new analysis will particularly open new doors within the field of epidemiological modelling, which will aid researchers to better understand the spread of infectious diseases. The stochastic version of the suggested model was also investigated, and numerical simulations were performed. The obtained reproductive number, strength number, extinction of criticism together with numerical simulation, revealed that the field of fractional calculus will be stable will therefore have no significant effect soon.

scholarly journals New fractional approaches for n-polynomial P-convexity with applications in special function theory

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Shu-Bo Chen ◽  
Saima Rashid ◽  
Muhammad Aslam Noor ◽  
Zakia Hammouch ◽  
Yu-Ming Chu
Keyword(s):  
Fractional Calculus ◽  
Convex Functions ◽  
Special Functions ◽  
Real Life ◽  
Fractional Integrals ◽  
Digamma Function ◽  
Novel Approach ◽  
Inequality Theory ◽  
New Strategy ◽  
Significant Mechanism

Abstract Inequality theory provides a significant mechanism for managing symmetrical aspects in real-life circumstances. The renowned distinguishing feature of integral inequalities and fractional calculus has a solid possibility to regulate continuous issues with high proficiency. This manuscript contributes to a captivating association of fractional calculus, special functions and convex functions. The authors develop a novel approach for investigating a new class of convex functions which is known as an n-polynomial $\mathcal{P}$ P -convex function. Meanwhile, considering two identities via generalized fractional integrals, provide several generalizations of the Hermite–Hadamard and Ostrowski type inequalities by employing the better approaches of Hölder and power-mean inequalities. By this new strategy, using the concept of n-polynomial $\mathcal{P}$ P -convexity we can evaluate several other classes of n-polynomial harmonically convex, n-polynomial convex, classical harmonically convex and classical convex functions as particular cases. In order to investigate the efficiency and supremacy of the suggested scheme regarding the fractional calculus, special functions and n-polynomial $\mathcal{P}$ P -convexity, we present two applications for the modified Bessel function and $\mathfrak{q}$ q -digamma function. Finally, these outcomes can evaluate the possible symmetric roles of the criterion that express the real phenomena of the problem.

scholarly journals Engineering Mathematical Analysis Method for Productivity Rate in Linear Arrangement Serial Structure Automated Flow Assembly Line

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Tan Chan Sin ◽  
Ryspek Usubamatov ◽  
M. A. Fairuz ◽  
Mohd Fidzwan B. Md. Amin Hamzas ◽  
Low Kin Wai
Keyword(s):  
Mathematical Model ◽  
Failure Rate ◽  
Mathematical Analysis ◽  
Assembly Line ◽  
Flow Line ◽  
Analysis Method ◽  
Machining Time ◽  
Linear Arrangement ◽  
Final Assembly ◽  
Productivity Rate

Productivity rate (Q) or production rate is one of the important indicator criteria for industrial engineer to improve the system and finish good output in production or assembly line. Mathematical and statistical analysis method is required to be applied for productivity rate in industry visual overviews of the failure factors and further improvement within the production line especially for automated flow line since it is complicated. Mathematical model of productivity rate in linear arrangement serial structure automated flow line with different failure rate and bottleneck machining time parameters becomes the basic model for this productivity analysis. This paper presents the engineering mathematical analysis method which is applied in an automotive company which possesses automated flow assembly line in final assembly line to produce motorcycle in Malaysia. DCAS engineering and mathematical analysis method that consists of four stages known as data collection, calculation and comparison, analysis, and sustainable improvement is used to analyze productivity in automated flow assembly line based on particular mathematical model. Variety of failure rate that causes loss of productivity and bottleneck machining time is shown specifically in mathematic figure and presents the sustainable solution for productivity improvement for this final assembly automated flow line.

Some Steffensen-type inequalities

2017 ◽  
Vol 8 (3) ◽  
Author(s):  
Mohammad W. Alomari ◽  
Sabir Hussain ◽  
Zheng Liu
Keyword(s):  
Integral Inequality ◽  
New Inequalities

AbstractIn this paper, new inequalities connected with the celebrated Steffensen’s integral inequality are proved.

scholarly journals Mathematical simulation of BF hot blast temperature influence on variations of silicon content in hot metal

2018 ◽  
pp. 25-31
Author(s):  
P. P. Semenyuk ◽  
R. E. Velikotsky ◽  
N. A. Rumyantseva
Keyword(s):  
Mathematical Model ◽  
Mathematical Analysis ◽  
Silicon Content ◽  
Statistical Data ◽  
Hot Metal ◽  
Blast Temperature ◽  
Mathematical And Computer Simulation ◽  
Hot Blast ◽  
Operation Results ◽  
Steel Works

The problem of influence of sinter production technological factors on silicon content and particularly variations of Si (ΔSi) in hot metal is actual for the up-to-date metallurgy.Traditional methods and plans of studies of BF heat running at present are considered less precise and effective comparing with up-to-date methods of mathematical and computer simulation, since the last provide an ability to forecast and optimize numerous parameters of BF process.A complex mathematical analysis of dependence between hot blast temperature and ΔSi by application of the universal mathematical model, specially elaborated and adapted for industrial conditions of sinter plant operation of Alchevsk steel-works was the task of the study.Influence of hot blast temperature (X-Factory) on minimization of ΔSi (Y-Factory) studied. Complex mathematical analysis was carried out using statistical data collected during 65 months of Alchevsk steel-works blast furnace of 3000 m3 operation. Results of calculation of influence of hot blast temperature on ΔSi by application of the universal mathematical model presented. Minimization of ΔSi when optimizing hot blast temperature reached. Accuracy of calculation using the elaborated model was more 99% of actual operational statistic.

scholarly journals Mathematical Analysis of an Autoimmune Diseases Model: Kinetic Approach

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1024 ◽  
Author(s):  
Mikhail Kolev
Keyword(s):  
Mathematical Model ◽  
Autoimmune Disease ◽  
Kinetic Theory ◽  
Autoimmune Diseases ◽  
Functional State ◽  
Mathematical Analysis ◽  
Numerical Results ◽  
Kinetic Approach ◽  
Basic Information ◽  
View Point

A new mathematical model of a general autoimmune disease is presented. Basic information about autoimmune diseases is given and illustrated with examples. The model is developed by using ideas from the kinetic theory describing individuals expressing certain functions. The modeled problem is formulated by ordinary and partial equations involving a variable for a functional state. Numerical results are presented and discussed from a medical view point.

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