Analytic Solution of Linear Fractional Differential Equation with Jumarie Derivative in Term of Mittag-Leffler Function [PDF]
American Journal of Mathematical Analysis, 2015, Vol. 3, No. 2,
32-38, 2015 There is no unified method to solve the fractional differential equation. The type of derivative here used in this paper is of Jumarie formulation, for the several differential equations studied. Here we develop an algorithm to solve the linear fractional differential equation composed via Jumarie fractional derivative in terms of Mittag-Leffler ...
arxiv +1 more source
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 +15 more
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On a New Class of Fractional Calculus of Variations and Related Fractional Differential Equations [PDF]
arXiv, 2021 This paper is concerned with analyzing a class of fractional calculus of variations problems and their associated Euler-Lagrange (fractional differential) equations. Unlike the existing fractional calculus of variations which is based on the classical notion of fractional derivatives, the fractional calculus of variations considered in this paper is ...
arxiv
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
On the Singular Perturbations for Fractional Differential Equation [PDF]
The Scientific World Journal, 2014 The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear ...
openaire +4 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 +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 +3 more
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Well-posedness of initial-boundary value problem for time-fractional diffusion-wave equation with time-dependent coefficients [PDF]
arXiv, 2022 We consider the well-posedness of the initial-boundary value problem for a time-fractional partial differential equation with the fractional order lying in (1,2]. First, we show some results on the unique existence of solution to time-fractional ordinary differential equations. Then the unique existence of weak and strong solutions to a time-fractional
arxiv
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 +19 more
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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
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