المجلد السابع

العدد الرابع عشر لشهر ديسمبر 2022

رجوع

تحميل البحث

full-text

الملخص:

في هذه المقالة، ناقشنا طريقة التحليل لـــAdomian decomposition method التي تمَّ تطبيقها لحل معادلة برنولي التفاضلية الكسرية الغير خطية (الخطية) من الدرجة الثانية مع الشروط الأولية. حيث يتم تحويل معادلة برنولي الكسرية إلى معادلة تفاضلية كسرية غير خطية (خطية) تخضع للشروط الأولية. ثم بحثنا عن وجود حلول تقريبية لهذا النوع من مشاكل القيمة الأولية من خلال تطبيق تقنية التحليلADM ، و ذلك من خلال دراسة بعض الأمثلة التوضيحية لتوضيح التقنية المقترحة و معرفة ما إذا كانت الطريقة المقدمة تظهر نتائج ذات كفاءة جيدة أم لا.

Abstract:

This research article discusses the Adomian decomposition method that has been applied to solving second-order the nonlinear (linear) fractional differential equation for the Bernoulli equation with initial conditions. Firstly, the Bernoulli equation with fractional derivatives is transferred to a nonlinear (linear) fractional differential equation subject to initial conditions. Then it investigated the existence of approximate solutions to this type of initial value problem by applying Adomian decomposition technique. In view of the convergence of this method, some illustrative examples are included to demonstrate the proposed technique and show the efficiency of the presented method.
Keywords: Fractional differential equation; Adomian decomposition method; Caputo fractional derivative; the Bernoulli differential equation with fractional derivative.

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