پديد آورنده :
فريدوني، الهه
عنوان :
حل عددي معادلات ديفرانسيل كسري تاخيري چندگانه با استفاده از توابع تركيبي بلاك - پالس و چند جمله اي هاي لژاندر
مقطع تحصيلي :
كارشناسي ارشد
گرايش تحصيلي :
رياضي كاربردي
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
صفحه شمار :
يازده، [۱۰۸]ص.: مصور، جدول
استاد راهنما :
حميدرضا مرزبان
واژه نامه :
انگليسي به فارسي; فارسي به انگليسي
توصيفگر ها :
معادلات ديفرانسيل كسري , حل تقريبي جواب ها , چند جمله اي هاي متعامد , سيستم هاي غيرخطي
استاد داور :
حميدرضا ظهوري زنگنه، محمود منجگاني
تاريخ ورود اطلاعات :
1396/11/08
چكيده انگليسي :
Numerical solution of fractional di erential equations with multi delays using hybrid of block pulse functions and Legendre polynomials Elaheh Fereidouni e fereidouni@math iut ac ir 2018 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Hamidreza Marzban hmarzban@cc iut ac ir 2010 MSC 34A08 34K28 42C05 93C10 Keywords Fractional di erential equations Numerical approximation of solutions Nonlinearsystems Orthogonal functions and polynomials AbstractFractional order dynamics appear in several problems in science and engineering such as viscoelasticmaterials economics continuum and statistical mechanics solid mechanics bioengineering dynamicsof interfaces between nanoparticles and substrates Although the optimal control theory is an area inmathematics that has been under development for many years the fractional optimal control theoryis a very new area in mathematics The control of systems with time delay has been of consider able concern Delays can be occurred in various elds including chemical biological economics andtransportation systems These systems and many physical systems are modeled by delay fractionaldi erential equations The delay fractional optimal control problem is an optimal control problem inwhich system dynamics are de ned with delay fractional di erential equations These problems ap pear in engineering economics power systems transportation biological electronics manufacturing chemical and many other elds However a few research works have been devoted to delay fractionaloptimal control problems It is worth noting that most of delay fractional optimal control problems donot have exact analytic solutions Consequently an e cient and robust numerical scheme has to beadopted In this thesis a new numerical method for solving delay fractional optimal control problemswith a quadratic performance index is presented Our approach is based on the direct method usinga hybrid of block pulse functions and orthonormal Taylor polynomials The set of hybrid functionsforms a complete set in the Hilbert space L2 0 tf Since the analytical solution associated with a delay
استاد راهنما :
حميدرضا مرزبان
استاد داور :
حميدرضا ظهوري زنگنه، محمود منجگاني
