Novel analytical and computational real and interval fractional calculi with applications / (Record no. 169741)
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| fixed length control field | 05807namaa22004211i 4500 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | OSt |
| 005 - أخر تعامل مع التسجيلة | |
| control field | 20250223033354.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 241225s2023 |||a|||f m||| 000 0 eng d |
| 040 ## - CATALOGING SOURCE | |
| Original cataloguing agency | EG-GICUC |
| Language of cataloging | eng |
| Transcribing agency | EG-GICUC |
| Modifying agency | EG-GICUC |
| Description conventions | rda |
| 041 0# - LANGUAGE CODE | |
| Language code of text/sound track or separate title | eng |
| Language code of summary or abstract | eng |
| -- | ara |
| 049 ## - Acquisition Source | |
| Acquisition Source | Deposit |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 515.62 |
| 092 ## - LOCALLY ASSIGNED DEWEY CALL NUMBER (OCLC) | |
| Classification number | 515.62 |
| Edition number | 21 |
| 097 ## - Degree | |
| Degree | Ph.D |
| 099 ## - LOCAL FREE-TEXT CALL NUMBER (OCLC) | |
| Local Call Number | Cai01.12.17.Ph.D.2023.He.N. |
| 100 0# - MAIN ENTRY--PERSONAL NAME | |
| Authority record control number or standard number | Hend Dawood, |
| Preparation | preparation. |
| 245 10 - TITLE STATEMENT | |
| Title | Novel analytical and computational real and interval fractional calculi with applications / |
| Remainder of title | |
| Statement of responsibility, etc. | By Hend Dawood; supervisors Prof. Dr. Laila Fahmy Abdelal, Dr. Nefertiti Megahed. |
| 246 15 - VARYING FORM OF TITLE | |
| Title proper/short title | نظرياتٌ تحليليةٌ وحسابيةٌ جديدةٌ لحسابِ التفاضلِ والتكاملِ الكسريِّ للدوالِ الحقيقيةِ والفتـريةِ وتطبيقاتُها / |
| 264 #0 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Date of production, publication, distribution, manufacture, or copyright notice | 2023. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 387 pages : |
| Other physical details | illustrations ; |
| Dimensions | 25 cm. + |
| Accompanying material | CD. |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Source | rda content |
| 337 ## - MEDIA TYPE | |
| Media type term | Unmediated |
| Source | rdamedia |
| 338 ## - CARRIER TYPE | |
| Carrier type term | volume |
| Source | rdacarrier |
| 502 ## - DISSERTATION NOTE | |
| Dissertation note | Thesis (Ph.D)-Cairo University, 2023. |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE | |
| Bibliography, etc. note | Bibliography: pages 337-366. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc. | Uncertainty arises in all fields of modern science. It is a state of limited knowledge where “To know” means “To be uncertain of”. Acquiring reliable knowledge amidst uncertainty is the raison d’être of the present dissertation. In this connexion, a worthwhile progress in fractional calculus is to introduce analytical and computational theories of fractional calculus that wholly address the computation of fractional derivatives and integrals under uncertainty. Motivated by an ever-increasing indeterminacy and complexity in physics and engineering and fueled by developments in computational and uncertainty mathematics, the main objectives of this dissertation are to lay out two generalized analytic theories of uncertain fractional calculus, addressing respectively: (1) verified enclosures of fractional derivatives and integrals of real functions, and (2) verified enclosures of fractional derivatives and integrals of interval functions; and to attempt to machine-realize these theories. Towards this aim, we develop a number of mathematical systems and many nice consequences come for free. The main contributions of this work are therefore three-fold: a “logico-algebraic formalization”, an “extension”, and a problem-independent “machine implementation” of fractional derivatives and integrals under uncertainty. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc. | عَدَمُ التَّيقُّنِ uncertainty يظهرُ جليًّا في كل مَناحِي العلومِ. هو حالةٌ من مَحدوديةِ المَعرفةِ يكونُ فيها "أن تَعرفَ to know" يعني "ألّا تَكونَ مُتيقنًا to be uncertain of". الحُصولُ على مَعرفةٍ مَوثُوقةٍ reliable knowledge في ظلِّ مُشكلةِ عدمِ التيقنِ هو جوهرُ raison d'être هذه الأطروحةِ. في هذا الإطارِ فإنَّ إسهامًا ذا قيمةٍ في حسابِ التفاضلِ والتكاملِ الكسريِّ هو تقديمُ نظرياتٍ تحليليةٍ analytical وحوسبيةٍ computational تعالجُ حساب التفاضلاتِ والتكاملاتِ الكسريةِ fractional derivatives and integrals في ظلِّ مشكلةِ عدم التيقنِ under uncertainty. وعليهِ فإن الهدفَ الرئيسَ لهذه الأطروحةِ هو تقديمُ نظريتين عامَّتين للتفاضل والتكامل الكسريِّ اللايقينيِّ uncertain fractional calculus. هاتان النظريتان الجديدتان تقدمان على الترتيبِ: (1) إدراجاتٍ موثوقةٍ verified enclosures للتفاضلات والتكاملات الكسرية للدوال الحقيقية real functions، (2) إدراجاتٍ موثوقة للتفاضلاتِ والتكاملات الكسرية للدوال الفترية interval functions. أيضًا تهدفُ الأطروحةُ لتقديم التنفيذ الحوسبيِّ machine implementation لهاتين النظريتين. سعيًا نحو هذه الأهدافِ جميعِها فإنّ الأطروحةَ تؤسسُ لعددٍ من البِنَى الرياضياتيةِ mathematical structures وتنشيءُ عددًا من النتائج ذاتِ القيمةِ nice consequences. على ذلك يكونُ هذا البحثُ ثلاثيَّ الجوانبِ three-fold: في جانبٍ هو صورنةٌ جبرُ-منطقيةٍ logico-algebraic formalization لحسابِ التفاضلِ والتكامل الكسريِّ حقيقيِّ الرتبة، وفي ثانٍ هو تعميمٌ extension لهذا الحساب، وفي جانبٍ ثالثٍ هو تنفيذٌ حوسبيٌّ عامٌ له غيرُ مرتبطٍ بمشكلةٍ بعينها a problem-independent machine implementation. |
| 530 ## - ADDITIONAL PHYSICAL FORM AVAILABLE NOTE | |
| Issues CD | Issues also as CD. |
| 546 ## - LANGUAGE NOTE | |
| Text Language | Text in English and abstract in English. |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Calculus |
| Source of heading or term | qrmak |
| 653 #0 - INDEX TERM--UNCONTROLLED | |
| Uncontrolled term | Uncertain fractional analysis |
| -- | Interval fractional analysis |
| -- | Verified fractional calculus |
| -- | Interval mathematics |
| -- | Interval analysis |
| -- | Guaranteed interval enclosures |
| -- | Interval automatic differentiation |
| -- | Interval Taylor models |
| -- | Set-valued algebras |
| -- | Uncertainty mathematics |
| -- | Verification mathematics |
| -- | Verified computations |
| -- | Machine implementation of fractional analysis |
| -- | InCLosure |
| 700 0# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Laila Fahmy Abdelal |
| Relator term | thesis advisor. |
| 700 0# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Nefertiti Megahed |
| Relator term | thesis advisor. |
| 900 ## - Thesis Information | |
| Grant date | 01-01-2023 |
| Supervisory body | Laila Fahmy Abdelal |
| -- | Nefertiti Megahed |
| Universities | Cairo University |
| Faculties | Faculty of Science |
| Department | Department of Mathematics |
| 905 ## - Cataloger and Reviser Names | |
| Cataloger Name | Sara Salah |
| Reviser Names | Huda |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Source of classification or shelving scheme | Dewey Decimal Classification |
| Koha item type | Thesis |
| Edition | 21 |
| Suppress in OPAC | No |
| Source of classification or shelving scheme | Home library | Current library | Date acquired | Inventory number | Full call number | Barcode | Date last seen | Effective from | Koha item type |
|---|---|---|---|---|---|---|---|---|---|
| Dewey Decimal Classification | المكتبة المركزبة الجديدة - جامعة القاهرة | قاعة الرسائل الجامعية - الدور الاول | 25.12.2024 | 89775 | Cai01.12.17.Ph.D.2023.He.N. | 01010110089775000 | 25.12.2024 | 25.12.2024 | Thesis |