Fractional Differential Equations

Explicit formula and graphs of few special functions are derived in the paper on the basis of various definitions of various fractional derivatives and various fractional integrals. Their applications are also reviewed in the paper.

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Applications of Fractional Calculus

Dual-wave solutions for the quadratic–cubic conformable-Caputo time-fractional Klein–Fock–Gordon equation

(G'/G)-Expansion Method for Solving Fractional Partial Differential Equations in the Theory of Mathematical Physics

Dynamical analysis of long-wave phenomena for the nonlinear conformable space-time fractional (2+1)-dimensional AKNS equation in water wave mechanics.

The present paper applies the exp ( − φ ( ξ ) ) -expansion and the extended tanh-function methods to the (2+1)-dimensional Heisenberg Ferromagnetic Spin Chain (HFSC) equation. The applied methods acquire some new exact traveling wave solutions to the HFSC equation, which are representing the hyperbolic, trigonometric, exponential and rational function solutions. All solutions exhibit distinct physical configurations, such as the periodic, dark and singular soliton solutions. Three dimensional (3D) and two dimensional (2D) cross sectional graphics of some obtained solutions are confirmed the periodic, dark and singular behaviors. Furthermore, the conformable derivative is also considered and discussed for aforesaid methods to the HFSC equation. As outcomes, some new optical solutions are also attained in terms of fractionality. Obtained new solutions ensured that aforesaid methods are the reliable treatment for seeking nonlinear phenomena to HFSC equation as well as any NLEEs arising in mathematical physics and fiber optics.

Construction of traveling wave solutions of the (2+1)-dimensional Heisenberg ferromagnetic spin chain equation

Wave solutions of the couple Drinfel'd–Sokolov–Wilson equation: new wave solutions and free parameters effect

In this paper, the -expansion method has been applied to find the new exact traveling wave solutions of the nonlinear evaluation equations (NLEEs) by utilizing 3rd-order Klein–Gordon Equation (KFGE). With the collaboration of symbolic commercial software maple, the competence of this method for inventing these exact solutions has been more exhibited. As an upshot, some new exact solutions are obtained and signified by hyperbolic function solutions, different combinations of trigonometric function solutions, and exponential function solutions. Moreover, the -expansion method is a more efficient method for exploring essential nonlinear waves that enrich a variety of dynamic models that arises in nonlinear fields. All sketching is given out to show the properties of the innovative explicit analytic solutions. Our proposed method is directed, succinct, and reasonably good for the various nonlinear evaluation equations (NLEEs) related treatment and mathematical physics also. 

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Md. Habibul Bashar

Papers

Dynamical analysis of long-wave phenomena for the nonlinear conformable space-time fractional (2+1)-dimensional AKNS equation in water wave mechanics.

Construction of traveling wave solutions of the (2+1)-dimensional Heisenberg ferromagnetic spin chain equation

Wave solutions of the couple Drinfel'd–Sokolov–Wilson equation: new wave solutions and free parameters effect

Exploration on traveling wave solutions to the 3rd-order klein–fock-gordon equation (KFGE) in mathematical physics

Influence of the Free Parameters and Obtained Wave Solutions from CBS Equation