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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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 ...
Małgorzata Klimek
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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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Fractional Differential Equations with the General Fractional Derivatives of Arbitrary Order in the Riemann–Liouville Sense [PDF]
Mathematics, 2022 In this paper, we first consider the general fractional derivatives of arbitrary order defined in the Riemann–Liouville sense. In particular, we deduce an explicit form of their null space and prove the second fundamental theorem of fractional calculus ...
Yuri Luchko
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Stability Properties of Multi-Term Fractional-Differential Equations
Fractal and Fractional, 2023 Necessary and sufficient stability and instability conditions are reviewed and extended for multi-term homogeneous linear fractional differential equations with Caputo derivatives and constant coefficients.
Oana Brandibur, Éva Kaslik
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De Computis, 2022 The fractional differential equations involving different types of fractional derivatives are currently used in many fields of science and engineering. Therefore, the first purpose of this study is to investigate the qualitative properties including the ...
K. Hattaf
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Extensions of some differential inequalities for fractional integro-differential equations via upper and lower solutions [PDF]
Қарағанды университетінің хабаршысы. Математика сериясы, 2023 This paper deals with some differential inequalities for generalized fractional integro-differential equations by using the technique of upper and lower solutions. The fractional differential operator is taken in Caputo’s sense and the nonlinear
A. Yakar, H. Kutlay
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