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作者:Mohammed Al-Refai , Thabet Abdeljawad
来源:[J].Advances in Difference Equations(IF 0.76), 2017, Vol.2017 (1)Springer
摘要:In this paper we study linear and nonlinear fractional diffusion equations with the Caputo fractional derivative of non-singular kernel that has been launched recently (Caputo and Fabrizio in Prog. Fract. Differ. Appl. 1(2):73-85, 2015 ). We first derive simple and strong maximum...
作者:Mohammed Al-Refai
来源:[J].Electronic Journal of Differential Equations(IF 0.426), 2018, Vol.2018 (36,), pp.1-10DOAJ
摘要:In this article we study linear and nonlinear differentialequations involving the Caputo fractional derivative with Mittag-Lefflernon-singular kernel of order $0<\alpha<1$.We first obtain a new estimate of the fractional derivative of a functionat its extreme points and derive a ...
作者:Mohammed Al-Refai , Mohamed Ali Hajji , Muhammad I. Syam
来源:[J].Abstract and Applied Analysis(IF 1.102), 2014, Vol.2014DOAJ
摘要:We introduce a simple and efficient series solution for a class of nonlinear fractional differential equations ofCaputo's type. The new approach is a modified form of the well-known Taylor series expansion where we overcome the difficulty of computing iterated fractional derivati...
作者:Mohammed Al-Refai , Nikos I. Kavallaris
来源:[J].Electronic Journal of Differential Equations(IF 0.426), 2006, Vol.2006 (29), pp.1DOAJ
摘要:A non-local elliptic equation, for which comparison methods are applicable, associated with Robin boundary conditions is considered. Upper and lower solutions for this problem are obtained by solving algebraic equations. These upper and lower solutions are used to obtain analytic...
作者:Mohammed Al-Refai
来源:[J].Electronic Journal of Qualitative Theory of Differential Equations(IF 0.74), 2012, Vol.2012 (55), pp.1-5DOAJ
摘要:We correct a recent result concerning the fractional derivative at extrema points. We then establish new results for the Caputo and Riemann-Liouville fractional derivatives at extrema points.
作者:Mohammed Al-Refai , Nikos I. Kavallaris
来源:[J].Electronic Journal of Differential Equations(IF 0.426), 2006, Vol.2006 (29), pp.1-16DOAJ
摘要:A non-local elliptic equation, for which comparison methods are applicable, associated with Robin boundary conditions is considered. Upper and lower solutions for this problem are obtained by solving algebraic equations. These upper and lower solutions are used to obtain analytic...
作者:Mohammed Al-Refai
来源:[J].Electronic Journal of Differential Equations(IF 0.426), 2012, Vol.2012 (191,), pp.1-12DOAJ
摘要:In this article, we discuss the basic theory of boundary-value problems of fractional order $1 < delta < 2$ involving the Caputo derivative. By applying the maximum principle, we obtain necessary conditions for the existence of eigenfunctions, and show analytical lower and upper ...
作者:Mohammed Al-Refai , Mohamed Ali Hajji ...
来源:[J].Abstract and Applied Analysis(IF 1.102), 2014, Vol.2014Hindawi
摘要:We introduce a simple and efficient series solution for a class of nonlinear fractional differential equations ofCaputo's type. The new approach is a modified form of the well-known Taylor series expansion where we overcome the difficulty of computing iterated fractional derivati...
作者:Moh’d Khier Al-Srihin , Mohammed Al-Refai , Thabet Abdeljawad
来源:[J].Discrete Dynamics in Nature and Society(IF 0.82), 2017, Vol.2017Hindawi
摘要:In this paper, we introduce an efficient series solution for a class of nonlinear multiterm fractional differential equations of Caputo type. The approach is a generalization to our recent work for single fractional differential equations. We extend the idea of the Taylor series ...
作者:Mohammed Al-Refai , Abdulla M. Jarrah
来源:[J].Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena(IF 1.246), 2019, Vol.126, pp.7-11Elsevier
摘要:Abstract(#br)In this paper, we define the weighted Caputo–Fabrizio fractional derivative of Caputo sense, and study related linear and nonlinear fractional differential equations. The solution of the linear fractional differential equation is obtained in a closed form, and h...

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