Multi-order fractional differential equations and their numerical solution

By Kai Diethelm, Neville J. Ford. Applied Mathematics and Computation, 2004

336 citations recorded by the source corpus.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/24001e72de12f65e27fb4d8924725793a907b73c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Ali H. Bhrawy
2. Mehdi Dehghan
3. Dumitru Băleanu
4. Mohsen Razzaghi
5. Yadollah Ordokhani
6. J. Machado
7. Abbas Saadatmandi
8. Changpin Li

In Modeling and Simulation

1. Ali H. Bhrawy
2. Dumitru Băleanu
3. Yadollah Ordokhani
4. Mehdi Dehghan
5. J. Machado
6. Weihua Deng
7. Changpin Li
8. Abbas Saadatmandi

In Numerical Analysis

1. Ali H. Bhrawy
2. Dumitru Băleanu
3. Yadollah Ordokhani
4. Mohsen Razzaghi
5. Mehdi Dehghan
6. Abbas Saadatmandi
7. J. Machado
8. Changpin Li

Citations in the corpus

• A new formula for fractional integrals of Chebyshev polynomials: Application for solving multi-term fractional differential equations (2013, background): “For the existence and uniqueness and continuous dependence of the solution of the problem, see [6].”
• Numerical analysis for distributed-order differential equations (2009, methodology): “The approach we propose to use in the examples is based on the method of [14, 15] and works as follows: first identify the greatest common divisor q of the orders of the derivatives on the left-hand side of (16) and the number 1.”
• Volterra integral equations and fractional calculus: Do neighboring solutions intersect? (2012, neutral): “, [6,8,9].”
• SOME EXISTENCE RESULTS FOR FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS WITH NONLINEAR CONDITIONS (2008, background): “For details, see [3, 4, 9, 11, 12] and the references therein.”
• Synchronization of fractional order chaotic systems using active control method (2012, methodology): “This scheme is the generalization of Adams–Bashforth–Moulton one [59,60].”
• Variational iteration method for the Burgers' flow with fractional derivatives—New Lagrange multipliers (2013, neutral): “Some numerical methods [1–6] and analytical methods [7–12] have been developed for fractional differential equations (FDEs).”
• Nonpolynomial collocation approximation of solutions to fractional differential equations (2013, background): “In each of these cases, we just have to transform our original equation into an equivalent system of fractional differential equations with order smaller than one (see [9] for details).”
• Numerical solution of fractional differential equations with a Tau method based on Legendre and Bernstein polynomials (2014, background): “The existence and uniqueness and continuous dependence of the solution to this problem are discussed in [42].”