یحییٰ اعظمی
ناظرین کو یہ معلوم کر کے افسوس ہوگا کہ دفتر دارالمصنفین کے منصرم یحییٰ صاحب اعظمی نے چند دنوں کی علالت کے بعد ۲۲؍ فروری کو انتقال کیا، وہ عمر بھر دارالمصنفین سے وابستہ رہے اور مرکر اس سے جدا ہوئے، مرحوم بڑے متدین اور دفتری کاموں میں تجربہ کار تھے، ہزاروں روپیے کا کاروبار ان کے ہاتھ میں تھا اور کبھی ایک حبہ کا فرق نہیں نکلتا تھا، ایسے قابل اعتماد آدمی مشکل سے ملیں گے، طبیعت میں حد سے زیادہ نظافت و نفاست تھی، بڑی صاف ستھری زندگی بسر کرتے تھے، ان کا دفتری کام بھی بڑا صاف ستھرا تھا، خشک دفتری کاموں کے ساتھ خوشگو شاعر بھی تھے، ان کے کلام کے دو مجموعے ’’نوائے حیات‘‘ اور ’’نوائے عصر‘‘ شائع ہوچکے ہیں، اﷲ تعالیٰ ان کی مغفرت فرمائے۔
(شاہ معین الدین ندوی، مارچ ۱۹۷۲ء)
Abdul Haq, India’s most popular researcher and literary figure, got retirement from the University of Delhi as dean of the Department of Urdu. For the very first time in India, he selected Iqbaliat as his doctorate topic. His books on Iqbaliat highlighted various unexplored topics and personalities. He presented and preached Iqbal’s thoughts and quotations exactly the way Iqbal wanted them to be presented. His articles on Iqbal always received great appreciation from all the literary circles and conferences in which he presented them. As a profound lover and having an understanding of Iqbal’s poetry, he gave new dimensions to his poetry, previously unknown to the world. Furthermore, as a researcher, he discussed numerous scholars who claimed to have an understanding of Iqbal’s poetry and analyzed their work critically. The current study is an acknowledgement of Professor Abdul Haq’s endeavors in the field of education, literature and his services for Iqbaliat. Moreover, the present study encompasses his written publications on the topic of Iqbaliat.
Space Spectral Time Fractional Finite Difference Method along with Stability Analysis for Fractional Order Nonlinear Wave Equations In this work, nonlinear partial differential equations governing the obscure phenomena of shallow water waves are discussed. Time fractional model is considered to understand the upcoming solutions on the basis of all historical states of the solution. A semi-analytic technique, Homotopy Perturbation Transform Method (HPTM) is used in conjunction with a numerical technique to validate the approximate solutions. With the aid of graphical interpretation, the favorable wave parameters, to avoid wave breaking are estimated. Afterwards, dynamical analysis of fractional order Schr dinger equation governing the optical wave propagation is reported in detail. The validity criteria for the application of the semi-analytic asymptotic methods are exploited. Comparison between the solutions obtained by the two asymptotic techniques, that is, the Fractional Homotopy Analysis Transform Method and the Optimal Homotopy Analysis Method is performed to select the most accurate technique for the stated problem. Space spectral analysis with integrating factor technique and time fraction finite difference method have been implemented to study the pressure waves propagating in bubbly fluids as well as nonlinear phenomena of plasma waves. Dynamical analysis of acoustic/pressure waves propagating in bubbly fluids is of great significance. Such flows arise in many engineering problems including sonochemistry, sonochemical reactors, cavitation around hydrofoils and ultrasonic propagation in medicine and biology. Fractional approach for modeling the propagation of the pressure waves in liquids containing a large number of tiny gas bubbles is proposed. Moreover, numerical solution of the fractional order Modified Korteweg-de Vries equation governing the dynamics is approximated using a novel space spectral time fractional finite difference tool. A spectral technique for space and a multi-step finite difference scheme for time are designed and implemented. The spatial spectral discretization error and the stability bounds are discussed. The nonlinear phenomena of plasma waves are well demonstrated with the aid of graphical analysis. Stability analysis of integer and fractional order KdV equations have been discussed quantitatively with the help of Evans function approximation.