A new second order approximation for fractional derivatives with applications

Other Title(s)

تقريب جديد من الدرجة الثانية للمشتقات الكسرية مع تطبيقاتها

Publication Date

2018-06-30

Country of Publication

Oman

No. of Pages

Main Subjects

Mathematics

English Abstract

We propose a generalized theory to construct higher order Grünwald type approximations for fractional derivatives.

We use this generalization to simplify the proofs of orders for existing approximation forms for the fractional derivative.

We also construct a set of higher order Grünwald type approximations for fractional derivatives in terms of a general real sequence and its generating function.

From this, a second order approximation with shift is shown to be useful in approximating steady state problems and time dependent fractional diffusion problems.

Stability and convergence for a Crank-Nicolson type scheme for this second order approximation are analyzed and are supported by numerical results.

Data Type

Conference Papers

Record ID

BIM-852453

American Psychological Association (APA)

Nasir, Hanifah Muhammad& Nafi, Kamal. 2018-06-30. A new second order approximation for fractional derivatives with applications. International Conference on Numerical Analysis and Optimization (4th : 2017 : Muscat, Oman). . Vol. 23, no. 1 (Special issue) (2018), pp.43-55.Muscat Oman : Sultan Qaboos University College of Science.
https://search.emarefa.net/detail/BIM-852453

Modern Language Association (MLA)

Nasir, Hanifah Muhammad& Nafi, Kamal. A new second order approximation for fractional derivatives with applications. . Muscat Oman : Sultan Qaboos University College of Science. 2018-06-30.
https://search.emarefa.net/detail/BIM-852453

American Medical Association (AMA)

Nasir, Hanifah Muhammad& Nafi, Kamal. A new second order approximation for fractional derivatives with applications. . International Conference on Numerical Analysis and Optimization (4th : 2017 : Muscat, Oman).
https://search.emarefa.net/detail/BIM-852453