Search or add a thesis

Advanced Search (Beta)
Home > Application of Fractional Calculus to Engineering: A New Computational Approach

Application of Fractional Calculus to Engineering: A New Computational Approach

Thesis Info

Access Option

External Link

Author

Zahoor, Raja Muhammad Asif

Program

PhD

Institute

International Islamic University

City

Islamabad

Province

Islamabad.

Country

Pakistan

Thesis Completing Year

2011

Thesis Completion Status

Completed

Subject

Applied Sciences

Language

English

Link

http://prr.hec.gov.pk/jspui/handle/123456789/343

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676725519288

Asian Research Index Whatsapp Chanel
Asian Research Index Whatsapp Chanel

Join our Whatsapp Channel to get regular updates.

Similar


In this dissertation, a new heuristic computational intelligence technique has been developed for the solution for fractional order systems in engineering. These systems are provided with generic ordinary linear and nonlinear differential equations involving integer and non-integer order derivatives. The design scheme consists of two parts, firstly, the strength of feed-forward artificial neural network (ANN) is exploited for approximate mathematical modeling and secondly, finding the optimal weights for ANN. The exponential function is used as an activation function due to availability of its fractional derivative. The linear combination of these networks defines an unsupervised error for the system. The error is reduced by selection of appropriate unknown weights, obtained by training the networks using heuristic techniques. The stochastic techniques applied are based on nature inspired heuristics like Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) algorithm. Such global search techniques are hybridized with efficient local search techniques for rapid convergence. The local optimizers used are Simulating Annealing (SA) and Pattern Search (PS) techniques. The methodology is validated by applying to a number of linear and nonlinear fraction differential equations with known solutions. The well known nonlinear fractional system in engineering based on Riccati differential equations and Bagley- Torvik Equations are also solved with the scheme. The comparative studies are carried out for training of weights for ANN networks with SA, PS, GA, PSO, GA hybrid with SA (GA-SA), GA hybrid with PS (GA-PS), PSO hybrid with SA (PSO-SA) and PSO hybrid with PS (PSO-PS) algorithms. It is found that the GA-SA, GA-PS, PSO-SA and PSO-PS hybrid approaches are the best stochastic optimizers. The comparison of results is made with available exact solution, approximate analytic solution and standard numerical solvers. It is found that in most of the cases the design scheme has produced the results in good agreement with state of art numerical solvers. The advantage of our approach over such solvers is that it provides the solution on continuous time inputs with finite interval instead of predefine discrete grid of inputs. The other perk up of the scheme in its simplicity of the concept, ease in use, efficiency, and effectiveness.
Loading...
Loading...

Similar Books

Loading...

Similar Chapters

Loading...

Similar News

Loading...

Similar Articles

Loading...

Similar Article Headings

Loading...

تم بن رہ سکتا ہوں

تم بن رہ سکتا ہوں

میرا دکھ تو میرا دکھ ہے
تیرا دکھ بھی میرا دکھ ہے
دونا دکھ بھی سہہ سکتا ہوں
کب میں تم بن رہ سکتا ہوں

بات مری تم مان بھی جائو
دل کی باتیں جان بھی جائو
تم کو کب کچھ کہہ سکتا ہوں
تم بِن اَب میں رہ سکتا ہوں

Moral Dichotomy: Coetzee’s Stance on Moral Dilemma in Postmodernist Society in Disgrace

Coetzee anticipates the moral dilemma of today's individuals, in order to achieve his aim torevert the current trends in moral philosophy which has marked morality with individual partialities. The morality of self/will has pervaded in the society with substantial philosophical argumentation as well. This research intends to study Dionysian morality in comparison with modern (Appolonian) principles of morality as presented by Coetzee. The research is planned to differentiate the two by presenting their roots with logical reasons; Nietzsche's conception of morality and the need of Freudian repression. In the context of Disgrace Coetzee developed his moral theory through circumstantial justice with such a force that all reasons given by Overman (Übermensch) of Nietzsche fail. The paper will unveil the relationship of power and the need for justice. Coetzee proves the importance of Freudian Repression Theory that makes everybody responsible for the concord in a society. The cultivation of Dionysian concept of life only brings disgrace to man, and such philosophies can only be supported when the individual is in power, vulnerability in the society makes man to understand the value of morality and exercise of proper judicial system. South Africal context of the novel situates the anticipation of Dionysian cult in more understanding way to the audience. To avoid social Darwinism, state institutions should come in action in order to ensure the equal power distribution among the masses. Uneven distribution of power creates only oppressors and victims in the society, which further lead society to chaos. Coetzee proves the importance of circumstantial justice over the institutional justice, as institutional justice can punish only but the transformation of transgressor only takes place with circumstantial justice and for the betterment of society, transformation provides better results than punishment because institutions do create a different power structures that also work to suppress people.

Genetic Analysis of Some Quality and Yield Contributing Traits in Bread Wheat under Drought Stress

Genetic analyses were conducted to understand the effect of drought in bread wheat. Genetic diversity is the base of any genetic improvement breeding program aimed at stress breeding. One hundred and five wheat genotypes were screened against drought stress using factorial completely randomized design at seedling stage. Significant variation was observed among all genotypes. Shoot length was non-significant and negatively correlated with all other traits except relative water content, so its selection seems not to be a promising criteria for this germplasm. Out of ten principal components (PCs), the first three PCs were significant under both conditions. They showed 74.6% and 76% variation under normal and drought conditions respectively. The ten drought tolerant and five drought susceptible genotypes were selected based on their performance and further analyzed in (10) line × tester (5) mating design for genetic studies. Among parents, the line G1-9493 (L1) and the tester G3-9508 (T1) proved good general combiners for most of the yield contributing traits under both environments. Among the crosses, the G1-9493×G3-9508 (L1×T1) was ideal specific combination for most of the quality and yield related traits under both conditions. Non-additive gene action was more prominent in the inheritance for traits studied. Using 95 SSR markers determined the gene diversity and polymorphic information content (PIC) values ranging from 0.41 and 0.33 to 0.90 and 0.89 respectively, indicating the significant level of genetic diversity. The maximum PIC value 0.89 and lowest PIC value 0.33 were found among the genomes A and D respectively. Genetic diversity among homeologous genomes ranked as: genome A> B> D, based upon PIC values. The studied genotypes divided into four genetically different subgroups based on STRUCTURE Bayesian and DARWIN analysis. According to this analysis, group 1, group 2 and group 3 had 2, 4 and 4 drought tolerant genotypes respectively while group 4 had 4 drought susceptible genotypes. The information generated through SSR markers showed their potentiality for determining genetic diversity and would be helpful in selecting desirable genotypes for obtaining promising results. The present investigations also showed a clear-cut identity of genotypes, which would be of great utility for the protection of Plant Breeder’s Rights. The superior genotype G1-9493 and cross G1-9493×G3-9508 can be combined to develop new promising and improved varieties under water stress conditions.