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On solutions of fractional Riccati differential equations

حول حلول المعادلات التفاضلية الكسرية ريكاتي

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 03 Feb 2017 Turkey Publisher:Springer Science and Business Media LLCJournal:Advances in Difference Equations, volume 2,017 (eissn: 1687-1847,

Authors: Mehmet Giyas Sakar; Ali Akgül; Dumitru Băleanu;

doi: 10.1186/s13662-017-1091-8 , 10.60692/pvjyp-64v89 , 10.60692/ka4r7-mw082

On solutions of fractional Riccati differential equations

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Abstract

We apply an itérative reproducing kernel Hilbert space method to get the solutions of fractional Riccati differential equations. L'analyse mise en œuvre dans ces formulaires de travail a une étape cruciale dans le processus de développement du calcul fractionnel. La dérivée fractionnelle est décrite dans le Caputo sense. Outcomes are demonstrated graphically and in tabulated forms to see the power of the method. Numerical experiments are illustrated to prove the ability of the method. Numerical results are compared with some existing methods.

We apply an iterative reproducing kernel Hilbert space method to get the solutions of fractional Riccati differential equations. The analysis implemented in this work forms a crucial step in the process of development of fractional calculus. The fractional derivative is described in the Caputo sense. Outcomes are demonstrated graphically and in tabulated forms to see the power of the method. Numerical experiments are illustrated to prove the ability of the method. Numerical results are compared with some existing methods.

We apply an iterative reproducing Hilbert space kernel method to get the solutions of fractional Riccati differential equations. The analysis implemented in this work forms a crucial step in the process of development of fractional calculus. The fractional derivative is described in the Caputo sense. Outcomes are demonstrated graphically and in tabulated forms to see the power of the method. Numerical experiments are illustrated to prove the ability of the method. Numerical results are compared with some existing methods.

We apply an iterative reproducing kernel Hilbert space method to get the solutions of fractional Riccati differential equations. The analysis implementad in this work forms a crucial step in the process of development of fractional calculus. The fractional derivative is descrid in the Caputo sense. Outcomes are demonstrated graphically and in tabulated forms to see the power of the method. Numerical experiments are illustrated to prove the ability of the method. Numerical results are compared with some existing methods.

نطبق طريقة نواة فضاء هيلبرت التكرارية للحصول على حلول المعادلات التفاضلية ريكاتي الجزئية. يشكل التحليل المنفذ في هذا العمل خطوة حاسمة في عملية تطوير حساب التفاضل والتكامل الكسري. يوصف المشتق الكسري بمعنى كابوتو. يتم عرض النتائج بيانياً وفي أشكال مجدولة لمعرفة قوة الطريقة. يتم توضيح التجارب العددية لإثبات قدرة الطريقة. تتم مقارنة النتائج العددية مع بعض الطرق الحالية.

Country

Turkey

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Keywords

inner product, Mathematical analysis, Convergence Analysis of Iterative Methods for Nonlinear Equations, Riccati equation, Differential equation, Numerical Methods for Singularly Perturbed Problems, FOS: Mathematics, iterative reproducing kernel Hilbert space method, Anomalous Diffusion Modeling and Analysis, Numerical Analysis, Algebra and Number Theory, Applied Mathematics, Fractional calculus, Hilbert space, Pure mathematics, Partial differential equation, Applied mathematics, Fractional Derivatives, Modeling and Simulation, Physical Sciences, Kernel (algebra), fractional Riccati differential equation, Fractional Calculus, analytic approximation, Iterative Methods, Analysis, Mathematics, Ordinary differential equation

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