In this paper, the fractional Sturm-Liouville problems, in which the second order derivative is replaced by a fractional derivative, are derived by the Homotopy perturbation method. The fractional derivatives are described in the Caputo sense. The present results can be implemented on the numerical solutions of the fractional diffusion-wave equations. Numerical results show that HPM is effectiv...

In this paper, we discuss nonlinear fractional difference equations with the Caputo like difference operator. Some asymptotic stability results of equations under investigated are obtained by employing Schauder fixed point theorem and discrete Arzela-Ascoli’s theorem. Three examples are also provided to illustrate our main results.

In the present paper we obtain closed form solutions of spacetime fractional telegraph equations using Adomian decomposition method. The space and time fractional derivatives are considered as Caputo fractional derivative and the solutions are obtained in terms of Mittag-Leffler functions.

We consider the fractional cable equation. For solution of fractional Cable equation involving Caputo fractional derivative, a new difference scheme is constructed based on Crank Nicholson difference scheme. We prove that the proposed method is unconditionally stable by using spectral stability technique.

In this paper, the improved Euler method is used for solving hybrid fuzzy fractional differential equations (HFFDE) of order q ∈ (0,1) under Caputo-type fuzzy fractional derivatives. This method is based on the fractional Euler method and generalized Taylor’s formula. The accuracy and efficiency of the proposed method is demonstrated by solving numerical examples.

0262-8856/$ see front matter 2009 Elsevier B.V. A doi:10.1016/j.imavis.2009.05.005 * Corresponding author. Address: IDIAP Research In Marconi 19, Martigny, Switzerland. Tel.: +41 277 217 E-mail addresses: [email protected] (B. Caputo), Hayman), [email protected] (M. Fritz), joe@n URLs: http://www.idiap.ch/bcaputo (B. Caputo), h darmstadt.de/mfritz (M. Fritz). Classifying materials from t...

The purpose of this paper is twofold. Firstly, we provide explicit and compact formulas for computing both Caputo and (modified) Riemann-Liouville (RL) fractional pseudospectral differentiation matrices (F-PSDMs) of any order at general Jacobi-Gauss-Lobatto (JGL) points. We show that in the Caputo case, it suffices to compute F-PSDM of order μ ∈ (0, 1) to compute that of any order k + μ with in...

Makalah ini membahas solusi sistem persamaan diferensial linier homogen fractional orde α dengan turunan Caputo. Bentuk umum diberikan dalam beberapa teorema dan contoh.Kata Kunci: Persamaan fractional, Caputo, Mittag-Leffler.