Results 51 to 60 of about 692,681 (370)

Fractional Integro-Differential Equations for Electromagnetic Waves in Dielectric Media

, 2011
We prove that the electromagnetic fields in dielectric media whose susceptibility follows a fractional power-law dependence in a wide frequency range can be described by differential equations with time derivatives of noninteger order.
A. A. Kilbas, A. A. Stanislavsky, A. Carpinteri, A. K. Jonscher, A. K. Jonscher, A. K. Jonscher, G. M. Zaslavsky, P. Debye, R. R. Nigmatullin, R. R. Nigmatullin, R. R. Nigmatullin, S. G. Samko, V. E. Tarasov, V. E. Tarasov, V. V. Novikov, Y. Yilmaz   +15 more
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Nonlocal Fractional Differential Equations and Applications [PDF]

Complex Analysis and Operator Theory, 2020
Boundary value problems for nonlocal fractional elliptic equations with parameter in Banach spaces are studied. Uniform $L_p$-separability properties and sharp resolvent estimates are obtained for elliptic equations in terms of fractional derivatives.
openaire   +3 more sources

Lie group classifications and exact solutions for time-fractional Burgers equation

, 2010
Lie group method provides an efficient tool to solve nonlinear partial differential equations. This paper suggests a fractional Lie group method for fractional partial differential equations.
A.B. Malinowska, G. Jmnarie, G.C. Wu, G.C. Wu, G.C. Wu, G.W. Bluman, Guo-Cheng Wu, P.J. Olver, R.K. Gazizov, Z.G. Deng   +9 more
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Existence of solutions for double-order Hilfer fractional boundary value problems at resonance

Journal of Hebei University of Science and Technology, 2022
In order to expand the basic theory of boundary value problems of fractional differential equations,the existence of solutions of double-order Hilfer fractional differential equations under Riemann-Stieltjes integral boundary conditions under resonance ...
Fanmeng MENG, Weihua JIANG, Chunjing GUO
doaj   +1 more source

Fractional Equations of Curie-von Schweidler and Gauss Laws

, 2008
The dielectric susceptibility of most materials follows a fractional power-law frequency dependence that is called the "universal" response. We prove that in the time domain this dependence gives differential equations with derivatives and integrals of ...
Barrett J H, Curie J, Curie J, Debye P, Debye P, Debye P, Erdelyi A, Gorenflo R, Gorenflo R, Jonscher A K, Jonscher A K, Jonscher A K, Kempfle S, Kilbas A A, Podlubny I, Ramakrishnan T V, Samko S G, Tuncer E, Vasily E Tarasov, von Schweidler E   +19 more
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On the oscillation of fractional differential equations

Fractional Calculus and Applied Analysis, 2012
In this paper we initiate the oscillation theory for fractional differential equations. Oscillation criteria are obtained for a class of nonlinear fractional differential equations of the form $$D_a^q x + f_1 (t,x) = v(t) + f_2 (t,x),\mathop {\lim }\limits_{t \to a} J_a^{1 - q} x(t) = b_1 $$ , where Daq denotes the Riemann-Liouville differential
Grace, Said R., Agarwal, Ravi P., Wong, Patricia Jia Yiing, Zafer, Ağacık   +3 more
openaire   +3 more sources

The General Fractional Derivative and Related Fractional Differential Equations

Mathematics, 2020
In this survey paper, we start with a discussion of the general fractional derivative (GFD) introduced by A. Kochubei in his recent publications. In particular, a connection of this derivative to the corresponding fractional integral and the Sonine ...
Yuri Luchko, Masahiro Yamamoto
semanticscholar   +1 more source

The closed-form solution by the exponential rational function method for the nonlinear variable-order fractional differential equations

Frontiers in Physics
The symmetry features of fractional differential equations allow effective explanation of physical and biological phenomena in nature. The generalized form of the fractional differential equations is the variable-order fractional differential equations ...
Mashael M. ALBaidani, Umair Ali, Abdul Hamid Ganie   +2 more
doaj   +1 more source

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

Applications of Fractional Differentiation Matrices in Solving Caputo Fractional Differential Equations

Fractal and Fractional, 2023
This paper pursues obtaining Jacobi spectral collocation methods to solve Caputo fractional differential equations numerically. We used the shifted Jacobi–Gauss–Lobatto or Jacobi–Gauss–Radau quadrature nodes as the collocation points and derived the ...
Zhongshu Wu, Xinxia Zhang, Jihan Wang, Xiaoyan Zeng   +3 more
doaj   +1 more source