Exact analytical soliton solutions of the M-fractional Akbota equation

Abstract

In this paper we explore the new analytical soliton solutions of the truncated M-fractional nonlinear $(1+1)$ -dimensional Akbota equation by applying the ${exp}_a$ function technique, Sardar sub-equation and generalized kudryashov techniques. Akbota is an integrable equation which is Heisenberg ferromagnetic type equation and have much importance for the analysis of curve as well as surface geometry, in optics and in magnets. The obtained results are in the form of dark, bright, periodic and other soliton solutions. The gained results are verified as well as represented by two-dimensional, three-dimensional and contour graphs. The gained results are newer than the existing results in the literature due to the use of fractional derivative. The obtained results are very helpful in optical fibers, optics, telecommunications and other fields. Hence, the gained solutions are fruitful in the future study for these models. The used techniques provide the different variety of solutions. At the end, the applied techniques are simple, fruitful and reliable to solve the other models in mathematical physics.

Keywords: exp a function technique; Analytical soliton solutions; Fractional Akbota equation; Generalized Kudryashov technique; Sardar sub-equation technique.