الحلول شبه التحليلية لمعادلات فيشر الكسرية للزمن عبر الطريقة التكرارية الجديدة
محتوى المقالة الرئيسي
الملخص
إحدى الطرق الفعالة لحل المعادلات التفاضلية الجزئية غير الخطية ذات المشتقات الكسرية هي الطريقة التكرارية لتحويل سومودو الجديدة (NSTIM). إنه يبرع في حل الألغاز الرياضية الصعبة ويقدم معلومات ثاقبة حول سلوك معادلات فيشر ذات الكسر الزمني. الطريقة، التي تستخدم مشتقات كابوتو الحسية وWolfram في Mathematica، موثوقة وسهلة الاستخدام وتعطي تصويرًا مرئيًا للحل. أظهرت النتائج التحليلية أن الطريقة المقترحة فعالة وبسيطة في توليد حلول دقيقة لمعادلات فيشر الكسرية للزمن. أصبحت النتائج أكثر موثوقية وقابلة للتطبيق من خلال تضمين مشتقات كابوتو الحسية. تعتمد النمذجة الرياضية على فعالية وبساطة منهج NSTIM لحل معادلات فيشر ذات الكسر الزمني لأنها تتيح حلولاً دقيقة دون استخدام الكثير من قوة المعالجة. يعد نهج NSTIM أداة مفيدة للباحثين في مجموعة متنوعة من المجالات لأنه يوفر أيضًا إطارًا مرنًا يمكن تعديله بسهولة مع المعادلات التفاضلية الكسرية الأخرى. أصبح من الممكن الآن فحص ديناميكيات وسلوك الأنظمة المعقدة التي تحكمها معادلات فيشر الكسرية الزمنية بكفاءة وموثوقية، مما يفتح طرقًا بحثية جديدة. إن القدرة على حل معادلات فيشر ذات الكسور الزمنية بكفاءة وموثوقية باستخدام نهج NSTIM لها آثار مهمة على مجالات مختلفة مثل الديناميات السكانية والبيولوجيا الرياضية وعلم الأوبئة. يمكن للباحثين الآن تحليل انتشار الأمراض أو دراسة الديناميكيات السكانية للأنواع بدقة أعلى وجهد حسابي أقل. يمهد هذا التقدم في حل المعادلات التفاضلية الكسرية الطريق لرؤى أعمق حول سلوك وأنماط الأنظمة المعقدة، مما يؤدي في نهاية المطاف إلى تعزيز الفهم العلمي وتقديم إمكانيات جديدة للتطبيقات العملية.
Received 27/05/2023,
Revised 15/10/2023,
Accepted 17/10/2023,
Published Online First 25/12/2023
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