Results 31 to 40 of about 282,929 (321)

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

Generalised Fractional Evolution Equations of Caputo Type [PDF]

, 2017
This paper is devoted to the study of generalised time-fractional evolution equations involving Caputo type derivatives. Using analytical methods and probabilistic arguments we obtain well-posedness results and stochastic representations for the ...
Hernández-Hernández, M. E., Kolokoltsov, V. N., Toniazzi, L.   +2 more
core   +2 more sources

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

A Comparative Study of the Fractional Partial Differential Equations via Novel Transform

Symmetry, 2023
In comparison to fractional-order differential equations, integer-order differential equations generally fail to properly explain a variety of phenomena in numerous branches of science and engineering.
A. Ganie, M. Albaidani, Adnan Khan
semanticscholar   +1 more source

An efficient algorithm for some highly nonlinear fractional PDEs in mathematical physics. [PDF]

PLoS ONE, 2014
In this paper, a fractional complex transform (FCT) is used to convert the given fractional partial differential equations (FPDEs) into corresponding partial differential equations (PDEs) and subsequently Reduced Differential Transform Method (RDTM) is ...
Jamshad Ahmad, Syed Tauseef Mohyud-Din
doaj   +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

An Efficient Technique of Fractional-Order Physical Models Involving ρ-Laplace Transform

Mathematics, 2022
In this article, the ρ-Laplace transform is paired with a new iterative method to create a new hybrid methodology known as the new iterative transform method (NITM).
Nehad Ali Shah, Ioannis Dassios, Essam R. El-Zahar, Jae Dong Chung   +3 more
doaj   +1 more source

A Reliable Technique for Solving Fractional Partial Differential Equation

Axioms, 2022
The development of numeric-analytic solutions and the construction of fractional-order mathematical models for practical issues are of the greatest importance in a variety of applied mathematics, physics, and engineering problems. The Laplace residual-power-series method (LRPSM), a new and dependable technique for resolving fractional partial ...
Azzh Saad Alshehry, Rasool Shah, Nehad Ali Shah, Ioannis Dassios   +3 more
openaire   +2 more sources

OSCILLATORY BEHAVIOR OF A FRACTIONAL PARTIAL DIFFERENTIAL EQUATION

Journal of Applied Analysis & Computation, 2018
Summary: In this paper, a fractional partial differential equation subject to the Robin boundary condition is considered. Based on the properties of Riemann-Liouville fractional derivative and a generalized Riccati technique, we obtained sufficient conditions for oscillation of the solutions of such equation.
Wang, Jiangfeng, Meng, Fanwei
openaire   +1 more source

SOLVABILITY OF HYPERBOLIC FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS

Journal of Applied Analysis & Computation, 2017
Summary: The main purpose of this paper is to study the existence and uniqueness of solutions for the hyperbolic fractional differential equations with integral conditions. Under suitable assumptions, the results are established by using an energy integral method which is based on constructing an appropriate multiplier.
Akilandeeswari, Aruchamy, Balachandran, Krishnan, Annapoorani, Natarajan   +2 more
openaire   +1 more source