Displaying similar documents to “From Newton's equation to fractional diffusion and wave equations.”

Bifurcations of the time-fractional generalized coupled Hirota-Satsuma KdV system

Marwan Alquran, Kamel Al-Khaled, Mohammed Ali, Omar Abu Arqub (2017)

Waves, Wavelets and Fractals

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The Hirota-Satsuma model with fractional derivative is considered to provide some characteristics of memory embedded into the system. The modified system is analyzed analytically using a new technique called residual power series method. We observe thatwhen the value of memory index (time-fractional order) is close to zero, the solutions bifurcate and produce a wave-like pattern.

Modelling of Piezothermoelastic Beam with Fractional Order Derivative

Rajneesh Kumar, Poonam Sharma (2016)

Curved and Layered Structures

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This paper deals with the study of transverse vibrations in piezothermoelastic beam resonators with fractional order derivative. The fractional order theory of thermoelasticity developed by Sherief et al. [1] has been used to study the problem. The expressions for frequency shift and damping factor are derived for a thermo micro-electromechanical (MEM) and thermo nano-electromechanical (NEM) beam resonators clamped on one side and free on another. The effect of fractional order derivative...

IVPs for singular multi-term fractional differential equations with multiple base points and applications

Yuji Liu, Pinghua Yang (2014)

Applicationes Mathematicae

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The purpose of this paper is to study global existence and uniqueness of solutions of initial value problems for nonlinear fractional differential equations. By constructing a special Banach space and employing fixed-point theorems, some sufficient conditions are obtained for the global existence and uniqueness of solutions of this kind of equations involving Caputo fractional derivatives and multiple base points. We apply the results to solve the forced logistic model with multi-term...

A Poster about the Recent History of Fractional Calculus

Machado, Tenreiro, Kiryakova, Virginia, Mainardi, Francesco (2010)

Fractional Calculus and Applied Analysis

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MSC 2010: 26A33, 05C72, 33E12, 34A08, 34K37, 35R11, 60G22 In the last decades fractional calculus became an area of intense re-search and development. The accompanying poster illustrates the major contributions during the period 1966-2010.

On contraction principle applied to nonlinear fractional differential equations with derivatives of order α ∈ (0,1)

Małgorzata Klimek (2011)

Banach Center Publications

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One-term and multi-term fractional differential equations with a basic derivative of order α ∈ (0,1) are solved. The existence and uniqueness of the solution is proved by using the fixed point theorem and the equivalent norms designed for a given value of parameters and function space. The explicit form of the solution obeying the set of initial conditions is given.