A New Neumann Series Method for Solving a Family of Local Fractional Fredholm and Volterra Integral Equations

Abstract

We propose a new Neumann series method to solve a family of local fractional Fredholm and Volterra integral equations. The integral operator, which is used in our investigation, is of the local fractional integral operator type. Two illustrative examples show the accuracy and the reliability of the obtained results.

Local Fractional Variational Iteration Method for Solving Volterra Integro-Differential Equations Within Local Fractional Operators

“…In this section, we recall briefly some basic theory of local fractional calculus and for more details, (Yang and Baleanu, 2012;Su et al, 2013;Yang et al, 2013a;2013b;2013c;Yang, 2012f;Wang et al, 2014;Yang et al, 2013d;Kilbas et al, 2006;Ma et al, 2013;Yang et al, 2013e;2013f;2013g).…”

Generalization of Hermite-Hadamard inequalities involving Hadamard fractional integrals

“…Inspired by the above interesting works, our group go on studying fractional version Hermite-Hadamard inequality involving Riemann-Liouville and Hadamard fractional integrals for all kinds of convex functions [9][10][11][12] and Işcan [13]. For other recent applications of fractional derivatives and fractional integrals, one can see [14][15][16][17][18][19].…”

Modelling Fractal Waves on Shallow Water Surfaces via Local Fractional Korteweg-de Vries Equation

“…However, there are certain nondifferentiable physical quantities describing the physical parameters locally, where the concept of differentiable functions is not applicable. In such cases the local fractional calculus (LFC) concept allows to obtain solutions adequate to such nondifferentiable problems [17][18][19][20][21][22][23][24][25] such as local fractional Helmholtz and diffusion equations [19], local fractional Navier-Stokes equations in fractal domain [21], local fractional Poisson and Laplace equations arising in the electrostatics in fractal domain [23], fractional models in forest gap [24], inhomogeneous local fractional wave equations [25], local fractional heat conduction equation [26], and other results [26][27][28][29][30].…”