Compatible extension of the -expansion approach for equations with conformable derivative

Area of Science:

• Nonlinear dynamics
• Mathematical physics
• Fractional calculus

Background:

• Nonlinear fractional evolution equations are crucial in modeling complex phenomena.
• Existing methods may lack efficiency or generalizability for these equations.

Purpose of the Study:

• To propose compatible extensions of the \(\text{m}\)-expansion and generalized \(\text{m}\)-expansion methods.
• To generate a wide range of closed-form solutions for nonlinear fractional evolution equations.

Main Methods:

• Utilizing extended \(\text{m}\)-expansion and generalized \(\text{m}\)-expansion schemes.
• Applying these methods to fractional space-time paired Burgers equations.
• Employing graphical representations for geometric interpretation of wave solutions.

Main Results:

• Achieved numerous novel closed-form solutions for the targeted equations.
• Demonstrated the effectiveness and simplicity of the proposed extensions.
• Obtained dissimilar solutions applicable to various nonlinear physical models.

Conclusions:

• The extended methods provide effective and direct approaches for solving nonlinear fractional evolution equations.
• The techniques are broadly applicable to diverse problems in mathematical physics involving conformable derivatives.