Inequalities for fractional differential equations [PDF]
Mathematical Inequalities & Applications, 2009 We consider some differential inequalities involving fractional derivatives in the sense of Riemann-Liouville. Bounds for theses fractional differential inequalities are found using desingularization techniques combined with some generalizations of Bihari-type inequalities. Some applications illustrating the usefulness of our results are also provided.
N. E. T Atar +2 more
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On fractional powers of the Bessel operator on a semiaxis
, 2018 In this paper we study fractional powers of the Bessel differential operator defined on a semiaxis. Some important properties of such fractional powers of the Bessel differential operator are proved.
Shishkina, E. L., Sitnik, S. M.
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A Fractional Lie Group Method For Anomalous Diffusion Equations [PDF]
, 2010 Lie group method provides an efficient tool to solve a differential equation. This paper suggests a fractional partner for fractional partial differential equations using a fractional characteristic method.
Wu, Guo-cheng
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Analytical solution with tanh-method and fractional sub-equation method for non-linear partial differential equations and corresponding fractional differential equation composed with Jumarie fractional derivative [PDF]
arXiv, 2015 The solution of non-linear differential equation, non-linear partial differential equation and non-linear fractional differential equation is current research in Applied Science. Here tanh-method and Fractional Sub-Equation methods are used to solve three non-linear differential equations and the corresponding fractional differential equation.
arxiv
Stationarity-conservation laws for certain linear fractional differential equations
, 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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FRACTIONAL LAPLACE TRANSFORM TO SOLVE CONFORMABLE DIFFERENTIAL EQUATIONS [PDF]
In this paper, we convert some of the conformable fractional differential equations (CFDEs) into ordinary differential equations using the fractional Laplace transform.
Dastmalchi Saei, Farhad +3 more
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Singular fractional differential equations [PDF]
PAMM, 2013 AbstractFractional differential equations have received increasing attention during recent years since the behavior of many physical systems can be properly described using the fractional order system theory.By fractional analog for Duhamel principle we give the existence‐uniqueness result for linear and nonlinear time fractional evolution equations ...
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ON THE FRACTIONAL RICCATI DIFFERENTIAL EQUATION [PDF]
International Journal of Pure and Apllied Mathematics, 2016 In this paper, We tried to find an analytical solution of nonlinear Riccati con- formable fractional differential equation. Fractional derivatives are described in the con- formable derivative. The behavior of the solutions and the effects of different values of frac- tional orderare presented graphically and table.
Mehmet Merdan, Tahir Khaniyev
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Solution of Conformable Fractional Ordinary Differential Equations via Differential Transform Method [PDF]
arXiv, 2016 Recently, a new fractional derivative called the conformable fractional derivative is given which is based on the basic limit definition of the derivative in [1]. Then, the fractional versions of chain rules, exponential functions, Gronwall's inequality, integration by parts, Taylor power series expansions is developed in [2].
arxiv
Linearized Asymptotic Stability for Fractional Differential Equations [PDF]
Electron. J. Qual. Theory Differ. Equ., No. 39, 1-13, 2016, 2015 We prove the theorem of linearized asymptotic stability for fractional differential equations. More precisely, we show that an equilibrium of a nonlinear Caputo fractional differential equation is asymptotically stable if its linearization at the equilibrium is asymptotically stable.
arxiv