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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

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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.
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محمد ثانی حسنی

محمد ثانی حسنی
ان سطروں کے لکھتے وقت مولانا سید ابوالحسن علی ندوی کے عزیز بھانجے جناب محمد ثانی حسنی کی وفات حسرت آیات کی اندوہناک خبر ملی، ان کو مولانا علی میاں اپنے فرزند کے برابر سمجھتے رہے، وہ اپنی متانت ، سنجیدگی اور خاموشی کی وجہ سے اپنے حلقہ میں بڑی قدر کی نظر سے دیکھے جاتے تھے، بڑے اچھے اہل قلم بھی تھے، ان کی کتابوں میں ایمانی حرارت و حمیت جلوہ گر رہتی تھی، ان کی وفات سے دارالمصنفین بھی سوگوار ہے، اس لیے بھی کہ یہاں جو سیمینار ہورہا ہے اس کے روح رواں مولانا علی میاں اور ان کے دست و بازو مولانا رابع ندوی تھے، جو مرحوم کے منجھلے بھائی تھے، ان کی سوگواری سے ہمارے سیمینار کی فضا بھی غم ناک رہے گی، دعا ہے کہ مرحوم کو کروٹ کروٹ جنت نعیم اور ان کے سوگوارماموں، بھائیوں اور بچوں کو صبر جمیل عطا ہو۔ (صباح الدین عبدالرحمن، فروری ۱۹۸۲ء)

 

اُسوہ نبوی ﷺ کی روشنی میں قیادت کےعصری تصورات In Contemporary Concepts of Leadership in the Light of the Holy Prophetﷺ )Analytical studies)

  *یاَیُّهَا الَّذِیْنَ اٰمَنُوْۤا اَطِیْعُوا اللّٰهَ وَ اَطِیْعُوا الرَّسُوْلَ وَ اُولِی الْاَمْرِ مِنْكُمْۚ* On a wide scale  There is a need for an ideal leader and his leadership. If a believer talks about leadership, he will only have the concept of Islamic leadership.  To which the verses and hadiths indicate, in this category there will be leaders and leaders who will be able to lead their supporters and followers towards physical and spiritual development. All kinds of leadership were given to the Prophet ﷺ.  Whatever qualities he had within him were of a perfect level. The principles of Islamic guidance that the Prophet ﷺ had explained were followed by the Companions and the pious people and any leadership in the whole universe that we see.  have also adopted it in full stubbornness, they emerged as the Ameerul  Momineen and Caliphate of the Muslims of that time, and the principle of following the leadership of the Prophet ﷺ, an Islamic state and society, equally for both Muslim and non-Muslim minorities.While the principles and laws of the current situation are completely opposite. The question is what are the goals and demands of the leadership of the present age and how is prophetic leadership helpful in the improvement of the current leadership?Are following the principles of leadership mentioned by Karim ﷺ? In the paper under discussion, contemporary leadership principles and their analyzes will be examined in the light of Prophet Muhammad  keeping in mind the requirements of the time.

رسول اللہ ﷺ کی عمال کودی گئی ہدایات کی روشنی میں گڈ گورننس کے اصول۔تحقیقی جائزہ

The Prophet (peace be upon him) appointed different governors from his companions in different areas as well as gave different instructions for governing and running the state. Same like Hazrat Ali from Najran ,Usaman Ibn Al-As from Taif,Khalid Bin Saeed from Kindah and Ziyad Bin Labeed(May Allah blessed them) from Hadhramaut etc. The most famous among these instructions is that were given to Hazrat Ma'ad ibn Jabal (RA). But these are scattered in different books of Hadith. In this thesis these instructions are compiled.So we could know that what is the rules of Islamic good governance. And also discussed that in which cities they sent and also discussed the geographical and historical details of those cities.