In this paper, we deduce a fractional-order model based on skin effect for frequency dependent transmission line model. The voltages and currents at any location in transmission line can be calculated by the proposed fractional partial differential equations. Then the fractional ordinary differential equation can obtained from the transmission line fractional partial differential equations thro...

In this paper, we presented a novel multi-strain TB model of variable-order fractional derivatives, which incorporates three strains: drug-sensitive, emerging multi-drug resistant (MDR) and extensively drug-resistant (XDR), as an extension for multi-strain TB model of nonlinear ordinary differential equations which developed in 2014 by Arino and Soliman [1]. Numerical simulations for this varia...

in this paper, we apply the local fractional laplace transform method (or yang-laplace transform) on volterra integro-differential equations of the second kind within the local fractional integral operators to obtain the analytical approximate solutions. the iteration procedure is based on local fractional derivative operators. this approach provides us with a convenient way to find a solution ...

Fractional differential equations are a natural generalization of ordinary differential equations. In the last few decades many authors pointed out that differential equations of fractional order are suitable for the metallization of various physical phenomena and that they have numerous applications in viscoelasticity, electrochemistry, control and electromagnetic, and so forth, see 1–4 . This...

*Correspondence: [email protected] 1Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok, 10800, Thailand 2Centre of Excellence in Mathematics, CHE, Sri Ayutthaya Road, Bangkok, 10400, Thailand Abstract In this article, we present some new existence and uniqueness results for nonlinear fractional integro-differential equations...

fractional calculus has been used to model physical and engineering processes that are found to be best described by fractional differential equations. therefore, a reliable and efficient technique as a solution is regarded.this paper develops approximate solutions for boundary value problems ofdifferential equations with non-integer order by using the shannon waveletbases. wavelet bases have d...

In this paper, a new approach to stability for fractional order control system is proposed. Here a dynamic system whose behavior can be modeled by means of differential equations involving fractional derivatives. Applying Laplace transforms to such equations, and assuming zero initial conditions, causes transfer functions with no integer powers of the Laplace transform variable s to appear. In ...

k , 0 ≤ k ≤ [α i ], 1 ≤ i ≤ n, where Dα ∗ denote Caputo fractional derivative. The RVIM, for differential equations of integer order is extended to derive approximate analytical solutions for systems of fractional differential equations. Advantage of the RVIM, is simplicity of the computations and convergent successive approximations without any restrictive assumptions or transform functions. S...