scholarly journals Some Hermite–Hadamard-Type Fractional Integral Inequalities Involving Twice-Differentiable Mappings

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2209
Author(s):  
Soubhagya Kumar Sahoo ◽  
Muhammad Tariq ◽  
Hijaz Ahmad ◽  
Ayman A. Aly ◽  
Bassem F. Felemban ◽  
...  
Keyword(s):  
Applied Sciences ◽  
Focal Point ◽  
Real Life ◽  
Integral Inequalities ◽  
Mathematical Science ◽  
Life Problems ◽  
Special Cases ◽  
Wide Range ◽  
Fractional Analysis ◽  
Almost All

The theory of fractional analysis has been a focal point of fascination for scientists in mathematical science, given its essential definitions, properties, and applications in handling real-life problems. In the last few decades, many mathematicians have shown their considerable interest in the theory of fractional calculus and convexity due to their wide range of applications in almost all branches of applied sciences, especially in numerical analysis, physics, and engineering. The objective of this article is to establish Hermite-Hadamard type integral inequalities by employing the k-Riemann-Liouville fractional operator and its refinements, whose absolute values are twice-differentiable h-convex functions. Moreover, we also present some special cases of our presented results for different types of convexities. Moreover, we also study how q-digamma functions can be applied to address the newly investigated results. Mathematical integral inequalities of this class and the arrangements associated have applications in diverse domains in which symmetry presents a salient role.

scholarly journals New Ostrowski-Type Fractional Integral Inequalities via Generalized Exponential-Type Convex Functions and Applications

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1429
Author(s):  
Soubhagya Kumar Sahoo ◽  
Muhammad Tariq ◽  
Hijaz Ahmad ◽  
Jamshed Nasir ◽  
Hassen Aydi ◽  
...  
Keyword(s):  
Fractional Integral ◽  
Great Part ◽  
Real Life ◽  
Strong Relationship ◽  
Integral Inequalities ◽  
Positive Real ◽  
New Class ◽  
Life Problems ◽  
Special Cases ◽  
Mathematical Sciences

Recently, fractional calculus has been the center of attraction for researchers in mathematical sciences because of its basic definitions, properties and applications in tackling real-life problems. The main purpose of this article is to present some fractional integral inequalities of Ostrowski type for a new class of convex mapping. Specifically, n–polynomial exponentially s–convex via fractional operator are established. Additionally, we present a new Hermite–Hadamard fractional integral inequality. Some special cases of the results are discussed as well. Due to the nature of convexity theory, there exists a strong relationship between convexity and symmetry. When working on either of the concepts, it can be applied to the other one as well. Integral inequalities concerned with convexity have a lot of applications in various fields of mathematics in which symmetry has a great part to play. Finally, in applications, some new limits for special means of positive real numbers and midpoint formula are given. These new outcomes yield a few generalizations of the earlier outcomes already published in the literature.

scholarly journals Fractional trapezium type inequalities for twice differentiable preinvex functions and their applications

2020 ◽  
Vol 10 (2) ◽  
pp. 226-236
Author(s):  
Artion Kashuri ◽  
Rozana Liko
Keyword(s):  
Integral Operator ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Recent Past ◽  
Trapezium Type ◽  
Special Means ◽  
Special Cases ◽  
Type Integral ◽  
Preinvex Functions ◽  
Almost All

Trapezoidal inequalities for functions of divers natures are useful in numerical computations. The authors have proved an identity for a generalized integral operator via twice differentiable preinvex function. By applying the established identity, the generalized trapezoidal type integral inequalities have been discovered. It is pointed out that the results of this research provide integral inequalities for almost all fractional integrals discovered in recent past decades. Various special cases have been identified. Some applications of presented results to special means have been analyzed. The ideas and techniques of this paper may stimulate further research.

Behavioral Study of Drosophila Fruit Fly and Its Modeling for Soft Computing Application

2016 ◽  
pp. 32-84 ◽  
Author(s):  
Tapan Kumar Singh ◽  
Kedar Nath Das
Keyword(s):  
Real Life ◽  
Optimal Solution ◽  
Fruit Fly ◽  
Linear Constraints ◽  
Behavioral Study ◽  
Search Optimization ◽  
Life Problems ◽  
Decision Variables ◽  
Wide Range ◽  
Real Life Situation

Most of the problems arise in real-life situation are complex natured. The level of the complexity increases due to the presence of highly non-linear constraints and increased number of decision variables. Finding the global solution for such complex problems is a greater challenge to the researchers. Fortunately, most of the time, bio-inspired techniques at least provide some near optimal solution, where the traditional methods become even completely handicapped. In this chapter, the behavioral study of a fly namely ‘Drosophila' has been presented. It is worth noting that, Drosophila uses it optimized behavior, particularly, when searches its food in the nature. Its behavior is modeled in to optimization and software is designed called Drosophila Food Search Optimization (DFO).The performance, DFO has been used to solve a wide range of both unconstrained and constrained benchmark function along with some of the real life problems. It is observed from the numerical results and analysis that DFO outperform the state of the art evolutionary techniques with faster convergence rate.

scholarly journals The origin of compression influences geometric instabilities in bilayers

2018 ◽  
Vol 474 (2217) ◽  
pp. 20180267 ◽  
Author(s):  
Sebastian Andres ◽  
Paul Steinmann ◽  
Silvia Budday
Keyword(s):  
Film Growth ◽  
Numerical Study ◽  
Real Life ◽  
Critical Conditions ◽  
Pattern Selection ◽  
Smart Surfaces ◽  
Life Problems ◽  
Wide Range ◽  
Post Buckling ◽  
The Impact

Geometric instabilities in bilayered structures control the surface morphology in a wide range of biological and technical systems. Depending on the application, different mechanisms induce compressive stresses in the bilayer. However, the impact of the chosen origin of compression on the critical conditions, post-buckling evolution and higher-order pattern selection remains insufficiently understood. Here, we conduct a numerical study on a finite-element set-up and systematically vary well-known factors contributing to pattern selection under the four main origins of compression: film growth, substrate shrinkage and whole-domain compression with and without pre-stretch. We find that the origin of compression determines the substrate stretch state at the primary instability point and thus significantly affects the critical buckling conditions. Similarly, it leads to different post-buckling evolutions and secondary instability patterns when the load further increases. Our results emphasize that future phase diagrams of geometric instabilities should incorporate not only the film thickness but also the origin of compression. Thoroughly understanding the influence of the origin of compression on geometric instabilities is crucial to solving real-life problems such as the engineering of smart surfaces or the diagnosis of neuronal disorders, which typically involve temporally or spatially combined origins of compression.

scholarly journals Different type parameterized inequalities via generalized integral operators with applications

2021 ◽  
Vol 66 (3) ◽  
pp. 423-440
Author(s):  
Artion Kashuri ◽  
Rozana Liko
Keyword(s):  
Integral Operator ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Recent Past ◽  
Special Means ◽  
Special Cases ◽  
Type Integral ◽  
Erentiable Function ◽  
Almost All

"The authors have proved an identity for a generalized integral operator via di erentiable function with parameters. By applying the established identity, the generalized trapezium, midpoint and Simpson type integral inequalities have been discovered. It is pointed out that the results of this research provide integral inequalities for almost all fractional integrals discovered in recent past decades. Various special cases have been identi ed. Some applications of presented results to special means and new error estimates for the trapezium and midpoint quadrature formula have been analyzed. The ideas and techniques of this paper may stimulate further research in the eld of integral inequalities."

scholarly journals Solving Real-Life Problems: Future Mobile Technology Sophistication

2016 ◽  
Vol 35 (3) ◽  
pp. 335-346
Author(s):  
Farhan Shafiq ◽  
Kamran Ahsan ◽  
Adnan Nadeem
Keyword(s):  
Disaster Management ◽  
Mobile Technology ◽  
Real Life ◽  
Vital Signs ◽  
Compensatory Mechanism ◽  
Management Domain ◽  
Process Procedures ◽  
Life Problems ◽  
Ease Of Access ◽  
Almost All

Almost all the human being real life concerned domains are taking advantage of latest technologies for enhancing their process, procedures and operations. This integration of technological innovations provides ease of access, flexibility, transparency, reliability and speed for the concerned process and procedures. Rapid growth of ICT (Information and Communication Technology) and MT (Mobile Technology) provides opportunity to redesign and reengineered the human routines’ life activities process and procedures. Technology integration and adoption in routine life activities may serves compensatory mechanism to assist the population in different manner such as monitoring older adults and children at homes, provides security assistance, monitoring and recording patients vital signs automatically, controlling and monitoring equipments and devices, providing assistance in shopping, banking and education as well. Disasters happened suddenly, destroy everything indiscriminately. Adoption and integration of latest technologies including ICT and MT can enhance the current disaster management process, procedures and operations. This research study focuses the impacts of latest and emerging technology trends in routine life activities and surrounds their potential strength to improve and enhance disaster management activities. MT is providing a promising platform for facilitating people to enhance their routine life activities. This research argue that integration and adoption of mobile computing in disaster management domain can enhance disaster management activities with promising minimizing error, quick information assembling, quick response based on technology manipulation and prioritizing action.

scholarly journals Mathematical Modeling for Routes and Cost of Local Transports in Pune City

2020 ◽  
Vol 9 (8) ◽  
pp. 25-28
Keyword(s):  
Transportation Problem ◽  
Real Life ◽  
Transportation Cost ◽  
Transportation Model ◽  
Air Suspension ◽  
Life Problems ◽  
Wide Range ◽  
Trip Distance ◽  
Research Domains

Transportation problem is considered a vitally important aspect that has been studied in a wide range of operations including research domains. As such, it has been used in simulation of several real life problems. The transportation model is for the optimization of routes, cost and travelling of peoples with the help of public transport buses from the source to the destination by road. The data is collected which includes number of trips per day, cost of trips per trip ,distance between source and destination etc. manually through the questionery interview with the conductors drivers and the regular travelling peoples travelling on that route as well as data collection from PMPML office and calculation for minimizing the transportation cost have been done. The result of the research with proper scheduling, proper routing of buses can save Rs. 48865.875 in a 1 day. The saving of the transportation cost increases the profit of the PMPML. The total saving amount profit percentage is about 18.15% increase from saving transportation cost. The parameters as discussed above are considered and collected manually with the help of survey sheet and transportation model is prepared and after that calculation for minimizing the transportation cost have been done. The methods used for minimization of transportation of cost are Northwest corner method, Least count method etc. The result of the research gives with proper scheduling, routing of buses can save generate so much of revenue with saving of cost.. The amount saved from the transportation cost is utilized for increase the facilities in bus such as A.C, Automatic door system, Air suspension, Good quality of seats etc.

scholarly journals Some integral inequalities for p-convex functions

Filomat ◽  
2016 ◽  
Vol 30 (9) ◽  
pp. 2435-2444
Author(s):  
Muhammad Noor ◽  
Muhammad Awan ◽  
Khalida Noor ◽  
Mihai Postolache
Keyword(s):  
Applied Sciences ◽  
Convex Functions ◽  
Integral Inequalities ◽  
Special Cases ◽  
Integral Identities

In this paper, we consider the class of p-convex functions. We derive some new integral inequalities of Hermite-Hadamard and Simpson type for differentiable p-convex functions using two new integral identities. Some special cases are also discussed. Interested readers may find novel and innovative applications of p-convex functions in various branches of pure and applied sciences. The ideas and techniques of this paper may stimulate further research in this field.

scholarly journals Efficient Three-Step Class of Eighth-Order Multiple Root Solvers and Their Dynamics

Symmetry ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 837
Author(s):  
R. A. Alharbey ◽  
Munish Kansal ◽  
Ramandeep Behl ◽  
J. A. Tenreiro Machado
Keyword(s):  
General Class ◽  
Real Life ◽  
Multiple Root ◽  
Order Convergence ◽  
Eighth Order ◽  
Dynamical Study ◽  
New Methods ◽  
Life Problems ◽  
Special Cases ◽  
New Strategy

This article proposes a wide general class of optimal eighth-order techniques for approximating multiple zeros of scalar nonlinear equations. The new strategy adopts a weight function with an approach involving the function-to-function ratio. An extensive convergence analysis is performed for the eighth-order convergence of the algorithm. It is verified that some of the existing techniques are special cases of the new scheme. The algorithms are tested in several real-life problems to check their accuracy and applicability. The results of the dynamical study confirm that the new methods are more stable and accurate than the existing schemes.

scholarly journals An Iteration Function Having Optimal Eighth-Order of Convergence for Multiple Roots and Local Convergence

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1419
Author(s):  
Ramandeep Behl ◽  
Ioannis K. Argyros ◽  
Michael Argyros ◽  
Mehdi Salimi ◽  
Arwa Jeza Alsolami
Keyword(s):  
Quantum Physics ◽  
Real Life ◽  
Chemical Reactor ◽  
Theoretical Models ◽  
Eighth Order ◽  
Multiple Zeros ◽  
Stirred Reactor ◽  
Life Problems ◽  
Special Cases ◽  
Iteration Functions

In the study of dynamics of physical systems an important role is played by symmetry principles. As an example in classical physics, symmetry plays a role in quantum physics, turbulence and similar theoretical models. We end up having to deal with an equation whose solution we desire to be in a closed form. But obtaining a solution in such form is achieved only in special cases. Hence, we resort to iterative schemes. There is where the novelty of our study lies, as well as our motivation for writing it. We have a very limited literature with eighth-order convergent iteration functions that can handle multiple zeros m≥1. Therefore, we suggest an eighth-order scheme for multiple zeros having optimal convergence along with fast convergence and uncomplicated structure. We develop an extensive convergence study in the main theorem that illustrates eighth-order convergence of our scheme. Finally, the applicability and comparison was illustrated on real life problems, e.g., Van der Waal’s equation of state, Chemical reactor with fractional conversion, continuous stirred reactor and multi-factor problems, etc., with existing schemes. These examples further show the superiority of our schemes over the earlier ones.

Sign in / Sign up

Export Citation Format

Share Document