Solution of conformable fractional ordinary differential equations via differential transform method [PDF]
Optik, 2017 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].
Unal, Emrah, Gokdogan, Ahmet
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Local discontinuous Galerkin methods for fractional ordinary differential equations [PDF]
BIT Numerical Mathematics, 2014 This paper discusses the upwinded local discontinuous Galerkin methods for the one-term/multi-term fractional ordinary differential equations (FODEs).
Deng, Weihua, Hesthaven, Jan S.
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Solution of fractional autonomous ordinary differential equations
Journal of Mathematics and Computer Science, 2021 Autonomous differential equations of fractional order and non-singular kernel are solved. While solutions can be obtained through numerical, graphical, or analytical solutions, we seek an implicit analytical solution.
AlAhmad, Rami +2 more
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Semilinear ordinary differential equation coupled with distributed order fractional differential equation [PDF]
Nonlinear Analysis: Theory, Methods & Applications, 2010 System of semilinear ordinary differential equation and fractional differential equation of distributed order is investigated and solved in a mild and classical sense. Such a system arises as a distributed derivative model of viscoelasticity and in the system identfica- tion theory.
Atanacković, Teodor +2 more
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NUMERICAL SOLUTION OF A LINEAR SYSTEM WITH A FRACTIONAL POWER [PDF]
Vestnik KRAUNC: Fiziko-Matematičeskie Nauki, 2013 We investigate numerical solutions of linear ordinary and partial differential equations. Cauchy’s problem for ordinary equations of first and second order are generalized with fractional power of finite operator.
I.A. Il’in +2 more
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On Lie Symmetry Analysis of Certain Coupled Fractional Ordinary Differential Equations [PDF]
Journal of Nonlinear Mathematical Physics, 2021 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sethukumarasamy, K. +2 more
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Approach of a class of discontinuous dynamical systems of fractional order: existence of the solutions [PDF]
, 2010 In this letter we are concerned with the possibility to approach the existence of solutions to a class of discontinuous dynamical systems of fractional order.
Aubin J.-P. +5 more
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Diffusive approximation of a time-fractional Burger's equation in nonlinear acoustics [PDF]
, 2016 A fractional time derivative is introduced into the Burger's equation to model losses of nonlinear waves. This term amounts to a time convolution product, which greatly penalizes the numerical modeling.
Lombard, Bruno, Matignon, Denis
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Improved ()-Expansion Method for the Space and Time Fractional Foam Drainage and KdV Equations
Abstract and Applied Analysis, 2013 The fractional complex transformation is used to transform nonlinear partial differential equations to nonlinear ordinary differential equations. The improved ()-expansion method is suggested to solve the space and time fractional foam drainage and KdV ...
Ali Akgül +2 more
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Journal of Applied Mathematics, 2014 Based on Jumarie’s modified Riemann-Liouville derivative, the fractional complex transformation is used to transform fractional differential equations to ordinary differential equations.
Wei Li, Huizhang Yang, Bin He
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