المجلد السابع

العدد الخامس عشر لشهر يونيو 2023

رجوع

تحميل البحث

full-text

الملخص:

الهدف من المقال هو دراسة وجود الحل التقريبي و وحدانيته لمشكلة القيمة الحدية لمعادلة شتورم لوﭬــــيل الكسرية مع المشتق Caputo في فضاء بنـاخ. حيث قمنا بإثبات بعض النظريات حول وجود الحل و تفرده لـــــ FSLP و من ثم قمنا بتوسيع نظرية النقطة الثابتة لـــــ ODEs لتشمل مشكلة Fractional Sturm-Liouville ذات الشروط الحدية، و بعد ذلك ثم الحصول على الحل التقريبي بواسطة الطرق التقريبية و هي طريقــــتي بيكـــارد و مان –كراسنوسلســـكى التكــرارية.

Abstract:

In this paper, the researcher investigated the Fractional Sturm–Liouville boundary value problem with the Caputo derivative and studied the existence and uniqueness of its solution in Banach space, in addition to the continuation of its solution. As the result, researcher proved some theorems on the existence of solutions for FSLP and then extend a Fixed-Point theorem for ODEs to this of the Fractional Sturm–Liouville problem with boundary conditions. Also, the given problem by obtained via the constructing approximate solution by Picard and Krasnoselskij-Mann iterations.
Keywords: Fractional Sturm–Liouville Problem, Caputo fractional derivatives, iterative methods, contraction and non-expansive mapping, Fixed-Point theorem.

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