Results 21 to 30 of about 4,216 (305)

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, D.S. Noshchenko, A.S. Perezhogin   +2 more
doaj   +1 more source

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, Oparnica, Ljubica, Pilipović, Stevan   +2 more
openaire   +2 more sources

Closed-form wave structures of the space-time fractional Hirota–Satsuma coupled KdV equation with nonlinear physical phenomena

Open Physics, 2020
The present paper applies the variation of (G′/G)(G^{\prime} /G)-expansion method on the space-time fractional Hirota–Satsuma coupled KdV equation with applications in physics. We employ the new approach to receive some closed form wave solutions for any
Alam Md Nur, Seadawy Aly R., Baleanu Dumitru   +2 more
doaj   +1 more source

Hyperbolic function solutions of time-fractional Kadomtsev-Petviashvili equation with variable-coefficients

AIMS Mathematics, 2022
Based on the variable separation method, the Kadomtsev-Petviashvili equation is transformed into a system of equations, in which one is a fractional ordinary differential equation with respect to time variable t, and the other is an integer order ...
Cheng Chen
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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, Adem Kılıçman, Mustafa Inc   +2 more
doaj   +1 more source

Exact Solutions of the Space-Time Fractional Bidirectional Wave Equations Using the (G′/G)-Expansion Method

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
doaj   +1 more source

The Use of Fractional B‐Splines Wavelets in Multiterms Fractional Ordinary Differential Equations [PDF]

International Journal of Differential Equations, 2009
We discuss the existence and uniqueness of the solutions of the nonhomogeneous linear differential equations of arbitrary positive real order by using the fractional B‐Splines wavelets and the Mittag‐Leffler function. The differential operators are taken in the Riemann‐Liouville sense and the initial values are zeros.
Huang, X., Lu, X.
openaire   +4 more sources

On the solution of some simple fractional differential equations

International Journal of Mathematics and Mathematical Sciences, 1990
The differintegration or fractional derivative of complex order ν, is a generalization of the ordinary concept of derivative of order n, from positive integer ν=n to complex values of ν, including also, for ν=−n a negative integer, the ordinary n-th ...
L. M. B. C. Campos
doaj   +1 more source

Fractional Complex Transform and exp-Function Methods for Fractional Differential Equations

Abstract and Applied Analysis, 2013
The exp-function method is presented for finding the exact solutions of nonlinear fractional equations. New solutions are constructed in fractional complex transform to convert fractional differential equations into ordinary differential equations.
Ahmet Bekir, Özkan Güner, Adem C. Cevikel   +2 more
doaj   +1 more source

The amazing fractional Maclaurin series for solving different types of fractional mathematical problems that arise in physics and engineering

Partial Differential Equations in Applied Mathematics, 2023
Many applications and natural phenomena in the fields of physics and engineering are described by ordinary and partial differential equations. Therefore, obtaining solutions to these equations helps to analyze and understand the dynamics of these systems,
Marwan Alquran
doaj   +1 more source