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An approximate solution of fractional order Riccati equations based on controlled Picard’s method with Atangana–Baleanu fractional derivative

Alexandria Engineering Journal • 2022
العودة
معلومات البحث
المؤلفون Fareed, A.F., Semary, M.S., Hassan, H.N.
الكلمات المفتاحية Fractional differential equations Atangana–Baleanu derivative Picard’s method Riccati equation
المجلة العلمية Alexandria Engineering Journal
الناشر Elsevier
المجلد 61
العدد 5
الصفحات 3673-3678
publication.type International
رابط البحث Open Link
المواد المرفقة Not Available
الملخص
In this paper, a new computationally efficient approach to solve fractional differential equations with Atangana–Baleanu operator is introduced. Controlled Picard’s method is employed for solving a class of fractional differential equations with order . The proposed approach can cover wide range of integer and fractional orders differential equations due to the extra auxiliary parameter which enhances the convergence and is suitable for nonlinear differential equations. Two models of fractional Riccati equation are solved to validate and illustrate the accuracy of the new approach. Figures has been used to construct the results obtained from the presented approach. It is shown that the proposed method is efficient, credible, and easy to implement for various related problems in science and engineering.