Results 51 to 60 of about 1,126,367 (350)

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
core   +1 more source

Approximate analytical solutions and applications of pantograph-type equations with Caputo derivative and variable orders

Applied Mathematics in Science and Engineering, 2023
This study presents an efficient method that is suitable for differential equations, both with integer-order and fractional derivatives. This study examines the construction of solutions of fractional differential equations that are associated with ...
M.O. Aibinu, E. Momoniat
doaj   +1 more source

Solutions of Sequential Conformable Fractional Differential Equations around an Ordinary Point and Conformable Fractional Hermite Differential Equation [PDF]

, 2015
In this work, we give the power series solutions around an ordinary point, in the case of variable coefficients, homogeneous sequential linear conformable fractional differential equations of order 2\alpha. Further, we introduce the conformable fractional Hermite differential equations, conformable fractional Hermite polynomials and basic properties of
arxiv   +1 more source

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
core   +1 more source

On fraction order modeling and control of dynamical systems [PDF]

, 2009
This paper demonstrates the feasibility of modeling any dynamical system using a set of fractional order di®erential equations, including distributed and lumped systems.
Kahalil, Islam, Naskali, Ahmet Teoman, Sabanovic, Asif, Şabanoviç, Asif   +3 more
core   +1 more source

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

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

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

Analytical Solutions for Multi-Time Scale Fractional Stochastic Differential Equations Driven by Fractional Brownian Motion and Their Applications

Entropy, 2018
In this paper, we investigate analytical solutions of multi-time scale fractional stochastic differential equations driven by fractional Brownian motions.
Xiao-Li Ding, Juan J. Nieto
doaj   +1 more source

Solutions of Fractional Differential Type Equations by Fixed Point Techniques for Multivalued Contractions

Complexity, 2021
This paper involves extended b−metric versions of a fractional differential equation, a system of fractional differential equations and two-dimensional (2D) linear Fredholm integral equations. By various given hypotheses, exciting results are established
Hasanen A. Hammad, Hassen Aydi, Manuel De la Sen   +2 more
doaj   +1 more source