Browsing by Author "Yang, X.-J."

Now showing 1 - 5 of 5

Citation - Scopus: 8
Advanced Analysis of Local Fractional Calculus Applied to the Rice Theory in Fractal Fracture Mechanics
(Springer Science and Business Media Deutschland GmbH, 2022) Yang, X.-J.; Baleanu, Dumitru; Baleanu, D.; Srivastava, H.M.; 56389; Matematik
In this chapter, the recent results for the analysis of local fractional calculus are considered for the first time. The local fractional derivative (LFD) and the local fractional integral (LFI) in the fractional (real and complex) sets, the series and transforms involving the Mittag-Leffler function defined on Cantor sets are introduced and reviewed. The uniqueness of the solutions of the local fractional differential and integral equations and the local fractional inequalities are considered in detail. The local fractional vector calculus is applied to describe the Rice theory in fractal fracture mechanics. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.
Citation - Scopus: 0
Advances On Integrodifferential Equations and Transforms
(Hindawi Publishing Corporation, 2015) Srivastava, H.M.; Baleanu, Dumitru; Yang, X.-J.; Baleanu, D.; Nieto, J.J.; Hristov, J.; 56389; Matematik
Citation - Scopus: 7
Initial-boundary value problems for local fractional laplace equation arising in fractal electrostatics
(L and H Scientific Publishing, LLC, 2015) Yang, X.-J.; Baleanu, Dumitru; Srivastava, H.M.; Baleanu, D.; 56389; Matematik
The initial-boundary value problems for the local fractional Laplace equation, which arises in fractal electrostatics, are investigated in this article. The non-differentiable solutions with different initial and boundary conditions are obtained by using the local fractional series expansion method. © 2015 L & H Scientific Publishing, LLC.
Citation - Scopus: 37
Local fractional variational iteration algorithms for the parabolic Fokker-Planck equation defined on cantor sets
(Natural Sciences Publishing, 2015) Baleanu, D.; Baleanu, Dumitru; Srivastava, H.M.; Yang, X.-J.; 56389; Matematik
In this article, we apply the local fractional variational iteration algorithms for solving the parabolic Fokker-Planck equation which is defined on Cantor sets. It is shown by comparing with the three LFVIAs that the LFVIA-II is the easiest to obtain the nondifferentiable solutions for linear local fractional partial differential equations. Several other related recent works dealing with local fractional derivative operators on Cantor sets are also indicated. © 2015 NSP.
Citation - Scopus: 1
On analytical methods for differential equations with local fractional derivative operators
(Nova Science Publishers, Inc., 2014) Yang, X.-J.; Baleanu, Dumitru; Baleanu, D.; Machado, J.A.T.; 56389; Matematik
This chapter reviews new analytical methods for a family of differential equations with local fractional derivatives. We concentrate mainly on Fourier series, and Fourier and Laplace transforms with local fractional operators. The potential applications of the reported results are discussed. © 2015 Nova Science Publishers, Inc.