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Some Important Aspects of Sharma-Mittal Holographic Dark Energy Model in Cherr-Simon Modified Gravity

Thesis Info

Author

Muhammad Hammad Waheed

Supervisor

Zulfiqar Ali

Program

Mphil

Institute

Riphah International University

Institute Type

Private

Campus Location

Faisalabad Campus

City

Faisalabad

Province

Punjab

Country

Pakistan

Thesis Completing Year

2019

Thesis Completion Status

Completed

Page

iv, 37 . : ill. ; 30 cm

Subject

Mathematics

Language

English

Other

Submitted in fulfillment of the requirements for the degree of M.Phil in Mathematics to the Faculty of Basic Science.; Includes bibliographical references; Thesis (M.Phil)--Riphah International University, 2019; English; Call No: 510 HAM

Added

2021-02-17 19:49:13

Modified

2023-02-19 12:33:56

ARI ID

1676711328928

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شیخ عبدالفتاح ابوغدہ

شیخ عبدالفتاح ابو غدہ
افسوس ہے کہ گزشتہ ماہ مشہور فاضل شیخ عبدالفتاح ابوغدہ ریاض میں انتقال فرماگئے، ان کی تدفین مدینہ منورہ کے معروف قبرستان جنت البقیع میں ہوئی، شیخ کا وطن شام کا مشہور شہر حلب تھا، ابتدائی تعلیم شام میں اور اعلیٰ تعلیم جامعہ ازہر مصر میں پائی۔ ایک عرصہ تک شام ہی میں درس و تدریس کی خدمت انجام دیتے رہے، ۱۹۶۴؁ء میں محمد بن سعود یونیورسٹی ریاض میں پروفیسر مقرر ہوئے تصنیف و تالیف سے مدۃالعمر سروکار رہا، حدیث و رجال پر انکی بڑی وسیع اور گہری نظر تھی، فقہ، تاریخ و ادب سے بھی دلچسپی تھی، مولانا عبدالحئی فرنگی محلی سے خاص شغف تھا، ان کی متعدد کتابیں ایڈٹ کیں۔ مولانا حبیب الرحمن الاعظمی کے علمی تبحر اور وسعت نظر کے بڑے معترف تھے، ممتاز عالم مولانا سیدابوالحسن علی ندوی سے ان کے مخلصانہ روابط تھے جن کی دعوت پر وہ کئی بار دارالعلوم ندوۃ العلماء لکھنو تشریف لائے اور اس کے اور ہندوستان کے دوسرے کتب خانوں سے استفادہ کیا، ان کے تلامذہ کا حلقہ وسیع تھا، جن میں ہندوستانی فضلا بھی شامل ہیں، شیخ ابوغدہ کی وفات بڑا علمی سانحہ ہے، اﷲ تعالیٰ دین و علم کے اس خادم کی مغفرت فرمائے۔ (ضیاء الدین اصلاحی۔ مارچ ۱۹۹۷ء)

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Mathematical Analysis and Control Strategies of Hiv-1 Infection Models

In this research, we will present mathematical analysis and optmal control strategies to control the spread of HIV-1 infection. For this, first we will develop a single delayed HIV-1 and discuss the effect of time delay in controlling HIV-1 infection. Once the complete dynamics of single delayed model is studied, we will extend this study to double delayed HIV-1 infection models. Incorporated time delays represent delay in contact process between pathogen virus and CD+4 cells (binding), latent period, virus production period and CTLs response. Then, to study the effect of dose-dependent infection rate in reducing HIV-1 infection, a new model is formulatedanditsstability willbediscussed. Themodelwillbeextendedbyincorporating the effect of recovery rate of unproductively infected cells to uninfected cells. Moreover, in order to reduce HIV-1 infection in the body, optimal control strategies will be developed. The aim of control strategies is to minimize the concentration of infected cells and maximize the concentration of uninfected cells. For this purpose optimal control variables will be incorporated in the proposed HIV-1 infection models with time delays and without time delays. To analyze the dynamical behavior of fractional order HIV-1 infection model, the proposed integer order HIV-1 models will be converted into fractional order model and its solution behavior will be discussed. Finally, to verify the derived theoretical results numerical simulations will be carried out for both integer and fraction order HIV-1 models.