Integral transforms suitable for solving fractional differential equations

Author:

Boiti ChiaraORCID,Franceschi Jonathan

Abstract

AbstractThe purpose of this article is to obtain appropriate tools for solving fractional differential equations that are flexible enough to adapt to different purposes. We thus look for a very general fractional Fourier transform with a phase function which can be appropriately chosen according to the problem you want to face.

Funder

Ministero dell’Università e della Ricerca

Università degli Studi di Ferrara

Publisher

Springer Science and Business Media LLC

Subject

General Mathematics

Reference8 articles.

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2. Lecture Notes in Mathematics;K Diethelm,2010

3. Franceschi, J.: A Study of Fractional Calculus Applicability to System Identification and Modeling for Control Design Purposes. Tesi di Laurea Magistrale in Matematica, Università degli Studi di Ferrara, Italy (Double Title with the “Master en Investigaciòn Matemàtica” of the Universitat de València and the Universitat Politècnica de València, Spain) (2021)

4. Kilbas, A.A.; Luchko, Y.F.; Martínez, H.; Trujillo, J.J.: Fractional Fourier transform in the framework of fractional calculus operators. Integr. Transforms Spec. Funct. 21, 779–795 (2010)

5. Luchko, Y.F.; Martínez, H.; Trujillo, J.J.: Fractional Fourier transform and some of its applications. Fract. Calc. Appl. Anal. 11(4), 457–470 (2008)

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