Solving partial fractional differential equations using the  | Zendy

Arman Aghili | Zendy; Alireza Ansari | Zendy

Open Access

Solving partial fractional differential equations using the <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct…

Author(s) -

Arman Aghili,

Alireza Ansari

Publication year - 2012

Publication title -

arab journal of mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.353

H-Index - 11

eISSN - 2588-9214

pISSN - 1319-5166

DOI - 10.1016/j.ajmsc.2012.05.001

Subject(s) - mathematics , integral transform , discrete fourier transform (general) , fractional fourier transform , affine transformation , fourier transform , pure mathematics , mathematical analysis , fourier analysis

In this article, we introduce the generalized Fourier transform (FA-transform) and derive an inversion formula and convolution product for this transform. Furthermore, the fundamental solutions of the single-order and distributed-order Cauchy type fractional diffusion equations are given by means of the appropriate FA-transform in terms of the Wright functions. Also, applicability of this transform for the explicit solution of the generalized Hilbert type singular integral equation is discussed

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