حل المعادلات التفاضلية الجزئية الكسرية باستخدام التحويلات الخطية المضاعفة
الشريط الجانبي للمقالة
محتوى المقالة الرئيسي
الملخص
في هذا البحث، استخدمنا طريقتي التحويلان التكامليان المضاعفان سمودو و الزاكي للحصول على الحلول العددية لبعض انواع المعادلات التفاضلية الجزئية الكسرية ذات المعاملات الثابتة، ووضحنا كفاءة الطريقة بتقديم بعض الامثلة العددية المحسوبة باستخدام برنامجي ماثكاد 15 و ماتلاب R2015a
تفاصيل المقالة
هذا العمل مرخص بموجب Creative Commons Attribution 4.0 International License.
كيفية الاقتباس
المراجع
Li Z, Liu L, Dehghan S, Chen Y, Xue DA. Review and evaluation of numerical tools for fractional calculus and fractional order controls. Int J control. 2017; 90(6): 1165—1181.
Jarad F , Tas K. Application of Sumudu and double Sumudu transforms to Caputo-fractional differential equations, J Comput Anal Appl. 2012;14(3): 475 – 483.
Eslaminasab M, Abbasbandy S. Study on usage of Elzaki transform for the ordinary differential equations with non-constant coefficients. IJIM 2015; 7(3): 277 – 282.
Tarik M, Salih M. On the Elzaki transform and ordinary differential equation with variable coefficients. Adv Theor App Math. 2011; 6(1): 41 – 46.
Tarik M, Salih M, Eman M. Elzaki and Sumudu transform for solving some differential equations. Glob. J. Pure Appl. Math. 2012; 8(2): 167 – 173.
Nuruddeen R, Lawal M, Nass A, Sulaimman T. A Review of the integral transforms-based decomposition methods and their applications in solving nonlinear partial differential equations. J Math. 2018; 7(1): 262-280.
Eltayeb H , Kiliçman A. On double Sumudu transform and double Laplace transform. Malayas J Math Sci. 2010; 4(1): 17-30.
Mehdi D. Application of fractional Calculus. J Math C Sc. 2010; 4(21):1021 – 1032.
Jun J, Yuqiang F, Shougui L. Exact solutions to the fractional differential equations with mixed partial derivatives. J Axioms. 2018; 7(10): 1 - 18.
Banu Y. Generalized Mittag-Leffler function and its properties. Ntmsci. 2015; 3(1): 12 – 18.
Rakash K. A class of extended Mittag-Leffler functions and their properties related to integral transforms and fractional calculus. J Math. 2015; 9(3):1069 – 1082.
Kilicman A , Gadian H. On the applications of Laplace and Sumudu transforms. J Franklin I. 2010; 3(7). 848 – 862.
HawJoon K. The time shifting theorem and the convolution for Elzaki transform. Int J App Math. 2013; 87(2):261 – 271.
Abaker A , Yagoub A. On double Elzaki transform and double Laplace transform. J Math. 2015; 11(1): 35 – 41.
Undegaonkar H. Similarity and comparison of Sumudu transform with Elzaki transform in solving ordinary differential equations with variable coefficients. Int J Math. 2017; 8(3): 66 – 69.
Fatima A, Eltayeb A, Arbab I. A new technique of Laplace variational iteration method for solving space-time fractional telegraph equations. Int J Diff Eq. 2013; 2(13): 1 – 10.