مجله مدل‌سازی پیشرفته ریاضی

مجله مدل‌سازی پیشرفته ریاضی

آنالیز وجود جواب معادلات دیفرانسیل غیرخطی ترکیبی شامل مشتق کوانتومی کسری

نوع مقاله : مقاله پژوهشی

نویسندگان
1 عضو هیات علمی گروه ریاضی دانشگاه آزاد
2 گروه ریاضی، دانشکده علوم پایه، دانشگاه بوعلی سینا، همدان، ایران
چکیده
در این مقاله به بررسی وجود جواب برای رده جدیدی از معادلات دیفرانسیل غیرخطی هیبریدی شامل مشتق کسری از نوع کوانتومی کاپوتو پرداخته می شود. با بهره گیری از ساختار هیبریدی این معادلات و ویژگی های خاص مشتق کسری کوانتومی، چارچوبی تحلیلی ارائه شده است که شرایط کافی برای تضمین وجود جواب را فراهم می کند. ابزار اصلی اثبات، قضیه نقطه ثابت پترشین است که با استفاده از آن، معیارهای لازم بر اساس خواصفضاهای باناخ و اپراتورهای فشرده‑پیوسته به دست آمده است. همچنین، چند مثال تحلیلی ارائه شده که نشان می دهد مدل پیشنهادی و شرایط وجود جواب به طور مؤثری قابل تحقق هستند. این مثال ها علاوه بر روشن سازی مراحل به کارگیری روش، اعتبار نتایج نظری به دست آمده را در زمینه کاربردی نیز تأیید می کنند. نتایج این پژوهش می تواند به عنوان پایه ای برای توسعه مطالعات بعدی در زمینه تحلیل کیفی و عددی معادلات دیفرانسیل کسری با ساختارهای پیچیده به کار گرفته شود.
کلیدواژه‌ها
موضوعات

عنوان مقاله English

Analysis of the existence of solutions to hybrid nonlinear differential equations including fractional q-derivative

نویسندگان English

Hamid Reza Sahebi 1
Mohammad Esmael Samei 2
1 Islamic Azad University
2 Department of Mathematics, Faculty of Science, Bu-Ali Sina University, Hamedan, Iran
چکیده English

In this paper, we investigate the existence of solutions for a novel class of nonlinear hybrid differential
equations involving the fractional quantum Caputo derivative. By exploiting the hybrid structure
of the considered equations and the distinctive properties of the fractional quantum derivative, an analytical
framework is established to derive sufficient conditions ensuring the existence of solutions. The proof
is based on Petryshyn’s fixed point theorem, employing the properties of spaces together with compact–
continuous operators. Several illustrative examples are provided to demonstrate the applicability of the
proposed model and to validate the theoretical results. Although explicit numerical values of the solutions
are not computed, the examples confirm that the proposed existence conditions are practically realizable.
The findings of this study serve as a foundation for further research in qualitative and numerical analysis
of fractional differential equations with complex hybrid structures.

کلیدواژه‌ها English

Quantum calculus
Caputo’s q-derivative
measure of non-compactness
Petryshyn fixed point theorem
nonlinear differential equations

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  • تاریخ دریافت 30 فروردین 1404
  • تاریخ بازنگری 03 شهریور 1404
  • تاریخ پذیرش 10 مهر 1404