معايير التذبذب للمعادلات التفاضلية المحايدة من الرتبة الثالثة ذات الرتبة الكسرية مع التخميد
الكلمات المفتاحية:
لمعادلات التفاضلية الكسرية، المعادلات المحايدة، التذبذب، التخميد، تحويل ريكاتيالملخص
تتناول هذه الورقة البحثية وضع معايير جديدة للتذبذب لفئة من المعادلات التفاضلية الكسرية المحايدة من الرتبة الثالثة ذات التخميد غير الخطي. ومن خلال توظيف تحويل ريكاتي الكسري المعدَّل بالاقتران مع تقنيات المتوسطات التكاملية ومشتقة كابوتو الكسرية، تم اشتقاق شروط كافية دقيقة تضمن تذبذب جميع الحلول. وتُعد النتائج المتحصل عليها تعميمًا وتحسينًا لعدد من معايير التذبذب المعروفة للمعادلات ذات الرتبة الصحيحة والرتبة الكسرية الواردة في الأدبيات العلمية. كما قُدِّم مثال توضيحي لبيان قابلية تطبيق النتائج النظرية المتوصل إليها.
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