Results 21 to 30 of about 182,739 (283)

The Existence and Uniqueness of Initial-Boundary Value Problems of the Fractional Caputo-Fabrizio Differential Equations

Universal Journal of Mathematics and Applications, 2019
In this paper, the existence and uniqueness problem of the initial and boundary value problems of the linear fractional Caputo-Fabrizio differential equation of order $\sigma \in (1,2]$ have been investigated.
Şuayip Toprakseven
doaj   +1 more source

On simple iterative fractional order differential equations [PDF]

, 2016
In this paper, the simple fractional iterative differential equation will be the focus of study Dβv(s)=vn(s), v(s0)=a. where s0, v0 ∈ I = [0, b], and 0 < β < 1.
Damag, Faten Hasan Mohammed, Kilicman, Adem   +1 more
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Asymptotic behavior of solutions of linear multi-order fractional differential equation systems

, 2017
In this paper, we investigate some aspects of the qualitative theory for multi-order fractional differential equation systems. First, we obtain a fundamental result on the existence and uniqueness for multi-order fractional differential equation systems.
Diethelm, Kai, Siegmund, Stefan, Tuan, H. T.   +2 more
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Neural fractional differential equations

Applied Mathematical Modelling
Fractional Differential Equations (FDEs) are essential tools for modelling complex systems in science and engineering. They extend the traditional concepts of differentiation and integration to non-integer orders, enabling a more precise representation of processes characterised by non-local and memory-dependent behaviours.
C. Coelho, M. Fernanda P. Costa, L.L. Ferrás   +2 more
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SEPARABLE LOCAL FRACTIONAL DIFFERENTIAL EQUATIONS [PDF]

Fractals, 2016
The concept of local fractional derivative was introduced in order to be able to study the local scaling behavior of functions. However it has turned out to be much more useful. It was found that simple equations involving these operators naturally incorporate the fractal sets into the equations.
openaire   +2 more sources

Application of two different algorithms to the approximate long water wave equation with conformable fractional derivative

Arab Journal of Basic and Applied Sciences, 2018
The current paper devoted on two different methods to find the exact solutions with various forms including hyperbolic, trigonometric, rational and exponential functions of fractional differential equations systems with conformable farctional derivative.
Melike Kaplan, Arzu Akbulut
doaj   +1 more source

Numerical solution of fractional Sturm-Liouville equation in integral form [PDF]

, 2014
In this paper a fractional differential equation of the Euler-Lagrange / Sturm-Liouville type is considered. The fractional equation with derivatives of order $\alpha \in \left( 0,1 \right]$ in the finite time interval is transformed to the integral form.
Blaszczyk, Tomasz, Ciesielski, Mariusz
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Fractional differential equations solved by using Mellin transform

, 2014
In this paper, the solution of the multi-order differential equations, by using Mellin Transform, is proposed. It is shown that the problem related to the shift of the real part of the argument of the transformed function, arising when the Mellin ...
Butera, Salvatore, Di Paola, Mario
core   +1 more source

Analysis of Fractional Differential Equations

Journal of Mathematical Analysis and Applications, 2002
The authors discuss the existence, uniqueness and structural stability of solutions to nonlinear differential equations of fractional order. They take the differential operators in the Riemann-Liouville sense and the initial conditions are specified according to Caputo's suggestion, in order to allow for an interpretation in a physically meaningful way.
Diethelm, Kai, Ford, Neville J.
openaire   +3 more sources

Semilinear ordinary differential equation coupled with distributed order fractional differential equation

, 2009
System of semilinear ordinary differential equation and fractional differential equation of distributed order is investigated and solved in a mild and classical sense.
Atanackovic, Teodor M., Oparnica, Ljubica, Pilipovic, Stevan   +2 more
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