Results 31 to 40 of about 3,658,718 (281)
Application of the Aboodh Transform for Solving Fractional Delay Differential Equations
Universal Journal of Mathematics and Applications, 2020 In this article, we extend the concept of the Aboodh transform to the solution of partial differential equations of fractional order using Caputo's fractional derivative.
Kacem Belghaba +1 more
doaj +1 more source
Advances in Difference Equations, 2017 We propose a new method called the fractional reduced differential transform method (FRDTM) to solve nonlinear fractional partial differential equations such as the space-time fractional Burgers equations and the time-fractional Cahn-Allen equation.
Mahmoud S Rawashdeh
doaj +1 more source
On a new class of fractional partial differential equations II [PDF]
Advances in Calculus of Variations, 2014 Abstract In this paper we continue to advance the theory regarding the Riesz fractional gradient in the calculus of variations and fractional partial differential equations begun in an earlier work of the same name. In particular, we here establish an
Shieh, Tien-Tsan, Spector, Daniel E.
openaire +5 more sources
Homotopy Analysis Method for Three Types of Fractional Partial Differential Equations
Complexity, 2020 In this paper, three types of fractional order partial differential equations, including the fractional Cauchy–Riemann equation, fractional acoustic wave equation, and two-dimensional space partial differential equation with time-fractional-order, are ...
Haidong Qu, Zihang She, Xuan Liu
doaj +1 more source
Multigrid methods for space fractional partial differential equations [PDF]
Journal of Computational Physics, 2015 We propose some multigrid methods for solving the algebraic systems resulting from finite element approximations of space fractional partial differential equations (SFPDEs). It is shown that our multigrid methods are optimal, which means the convergence rates of the methods are independent of the mesh size and mesh level.
Ying-Jun Jiang, Xuejun Xu
openaire +4 more sources
A Procedure to Construct Exact Solutions of Nonlinear Fractional Differential Equations
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
doaj +1 more source
Ain Shams Engineering Journal, 2014 In this paper, the fractional partial differential equations are defined by modified Riemann–Liouville fractional derivative. With the help of fractional derivative and traveling wave transformation, these equations can be converted into the nonlinear ...
Ahmet Bekir, Özkan Güner
doaj +1 more source
Journal of Taibah University for Science, 2022 In this study, the extended tanh-function method has been used to find further general travelling wave solutions for space-time fractional nonlinear partial differential equations, namely, the time fractional nonlinear Sine-Gordon equation and Klein ...
Umme Sadiya +3 more
doaj +1 more source
Converting fractional differential equations into partial differential equations
Thermal Science, 2012 A transform is suggested in this paper to convert fractional differential equations with the modified Riemann-Liouville derivative into partial differential equations, and it is concluded that the fractional order in fractional differential equations is equivalent to the fractal dimension.
Ji-Huan He, Zheng-Biao Li
openaire +1 more source
Weak Solutions for Time-Fractional Evolution Equations in Hilbert Spaces
Fractal and Fractional, 2021 Our purpose is to introduce a notion of weak solution for a class of abstract fractional differential equations. We point out that the time fractional derivative occurring in the equations is in the sense of the Caputo derivative.
Paola Loreti, Daniela Sforza
doaj +1 more source