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Fractional Calculus and Time-Fractional Differential Equations: Revisit and Construction of a Theory [PDF]
Mathematics, 2022 For fractional derivatives and time-fractional differential equations, we construct a framework on the basis of operator theory in fractional Sobolev spaces.
Masahiro Yamamoto
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A New Approach for Solving Nonlinear Fractional Ordinary Differential Equations
Mathematics, 2023 Recently, researchers have been interested in studying fractional differential equations and their solutions due to the wide range of their applications in many scientific fields.
Hassan Kamil Jassim +1 more
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Fractional Differential Equations [PDF]
International Journal of Differential Equations, 2010 1 School of Mathematical Sciences, Queensland University of Technology, P.O. Box 2434, Brisbane, Qeensland 4001, Australia 2 Department of Statistics and Probability, Michigan State University, A416 Wells Hall, East Lansing, MI 48823, USA 3 Department of Mathematics, Mu'tah University, P.O.
Fawang Liu +5 more
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Analysis of Fractional Differential Equations
Journal of Mathematical Analysis and Applications, 2002 AbstractWe discuss existence, uniqueness, and structural stability of solutions of nonlinear differential equations of fractional order. The differential operators are taken in the Riemann–Liouville sense and the initial conditions are specified according to Caputo's suggestion, thus allowing for interpretation in a physically meaningful way.
Diethelm, Kai, Ford, Neville J.
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The Laplace Transform Method for Linear Differential Equations of the Fractional Order [PDF]
In modified form included in Chapters 4 and 5 of the book:
Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego,
1999, 368 pages, ISBN 0125588402., 1997 The Laplace transform method for solving of a wide class of initial value problems for fractional differential equations is introduced. The method is based on the Laplace transform of the Mittag-Leffler function in two parameters. To extend the proposed method for the case of so-called "sequential" fractional differential equations, the Laplace ...
Igor Podlubný
arxiv +3 more sources
Stationarity-conservation laws for certain linear fractional differential equations [PDF]
, 2001 The Leibniz rule for fractional Riemann-Liouville derivative is studied in algebra of functions defined by Laplace convolution. This algebra and the derived Leibniz rule are used in construction of explicit form of stationary-conserved currents for ...
Douglas J F +16 more
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A Procedure to Construct Exact Solutions of Nonlinear Fractional Differential Equations [PDF]
The Scientific World Journal, 2014 We use the fractional transformation to convert the nonlinear partial fractional differential equations with the nonlinear ordinary differential equations.
Özkan Güner, Adem C. Cevikel
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Oscillation of a Class of Fractional Differential Equations with Damping Term [PDF]
The Scientific World Journal, 2013 We investigate the oscillation of a class of fractional differential equations with damping term. Based on a certain variable transformation, the fractional differential equations are converted into another differential equations of integer order with ...
Huizeng Qin, Bin Zheng
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On matrix fractional differential equations [PDF]
Advances in Mechanical Engineering, 2017 The aim of this article is to study the matrix fractional differential equations and to find the exact solution for system of matrix fractional differential equations in terms of Riemann–Liouville using Laplace transform method and convolution product to
Adem Kılıçman, Wasan Ajeel Ahmood
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Series expansion in fractional calculus and fractional differential equations [PDF]
arXiv, 2009 Fractional calculus is the calculus of differentiation and integration of non-integer orders. In a recently paper (Annals of Physics 323 (2008) 2756-2778), the Fundamental Theorem of Fractional Calculus is highlighted. Based on this theorem, in this paper we introduce fractional series expansion method to fractional calculus.
Ming-Fan Li, Ji-Rong Ren, Tao Zhu
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