A New Family of the Local Fractional PDEs

Issue title: Theory and Applications of Fractional Fourier Transform and its Variants

Guest editors: Yudong Zhang, Xiao-Jun Yang, Carlo Cattani, Zhengchao Dong, Ti-Fei Yuan and Liang-Xiu Han

Article type: Research Article

Authors: Yang, Xiao-Jun^{a; *} | Machado, J.A. Tenreiro^b | Nieto, Juan J.^{c; d}

Affiliations: [a] School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221116, People’s Republic of China. dyangxiaojun@163.com | [b] Institute of Engineering, Polytechnic of Porto, Department of Electrical Engineering, Rua Dr. António Bernardino de Almeida, 4249-015 Porto, Portugal | [c] Departamento de Analisis Matematico, Facultad de Matematicas, Universidad de Santiago de Compostela, 15782 Santiago, Spain | [d] Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Correspondence: [*] Address for correspondence: School of Mechanics and Civil Engineering China University of Mining and Technology, Xuzhou 221116, People’s Republic of China

Abstract: A new family of the local fractional PDEs is investigated in this article. The linear, quasilinear, semilinear and nonlinear local fractional PDEs are presented. Furthermore, three types of the local fractional PDEs are discussed, namely, parabolic, hyperbolic and elliptic. Several examples illustrate the corresponding models in nonlinear mathematical physics.

Keywords: local fractional PDE, parabolic PDE, hyperbolic PDE, elliptic PDE, local fractional derivative

DOI: 10.3233/FI-2017-1479

Journal: Fundamenta Informaticae, vol. 151, no. 1-4, pp. 63-75, 2017