Epistemology

Mathematical analysis

Chemistry

Philosophy

Biochemistry

Physics

Exponential function

Nonlinear system

Operator (biology)

Mathematics

Gene

Fractional calculus

Quantum mechanics

Exact solutions in general relativity

Simple (philosophy)

Transcription factor

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Applied mathematics

Mathematical Methods in the Applied Sciences

The paper aims to employ a new effective methodology to build exact fractional solutions to the generalized nonlinear Schrödinger equation with a local fractional operator defined on Cantor sets. The equation contains group velocity dispersion and second‐order spatiotemporal dispersion coefficients. We obtain exact solutions of the equation via the generalized version of the exponential rational function method. This new version of the method uses a set of elementary functions that are adopted on the contour set. To study the dynamic behavior of the obtained results, extensive numerical simulations are provided. We observe that the employed method is simple but quite efficient for determining the exact solutions of the problem in the local sense. Moreover, they are practically compatible with solving various classes of nonlinear problems arising in mathematical physics. All computations are carried out using the Maple package.

Abundant exact solutions to a generalized nonlinear Schrödinger equation with local fractional derivative