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کر کجھ اپنا آپ گمان
کر کجھ اپنا آپ گمان
پہلے اپنی ذات پچھان
توں ایں خالق دا شہکار
تیری سب توں اچی شان
تینوں عشق نے طاقت بخشی
توں بنیا حضرت انسان
تیرے اندر یار دا ڈیرہ
تیرے اندر کل جہان
تیری خاطر خلق اپائی
تیری خاطر جگ جہان
میرے نبیؐؐ دا نوکر بن
رب فرمایا وچ قرآن
تیرا رب شہ رگ توں نیڑے
تینوں دور کیتا شیطان
امیت رسول اور مستشرقین
Orientalists have always denied the acceptance of the divinity and authenticity of Qur’an. For this purpose, they have presented multifarious objections to prove the Qur’an as a discourse of Muhammad r which he learnt from the Christian monks and derived it from the judeo-Christian sources. They specially mention that Muhammad r was not an illiterate person he was rather a pupil of the monks. In this way, their aim is to prove false the claim of the miraculous (I’jaz) style of the Qur’an. We have proved in this study that according to Quran, Tafaseer and Hadiths of Prophet r, history and logic, that Muhammad r since his birth until his death, was illetrate, did not know how to read or write. In this paper, an effort has been made to examine the Western arguments and deduce the actual position in this matter. The basic and fundamental sources have been used to precede the discussion.Application of Fractional Calculus to Engineering: A New Computational Approach
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.Journals by Discipline
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