Adaptive Technique for Solving 1-D Interface Problems of Fractional Order

Area of Science:

• Numerical Analysis
• Fractional Calculus
• Applied Mathematics

Background:

• Fractional-order differential equations model complex phenomena.
• Solving 1-D interface problems with fractional orders presents analytical challenges.
• Existing methods often involve computationally intensive or complex terms.

Purpose of the Study:

• To present a novel numerical technique for solving one-dimensional (1-D) interface problems of fractional order.
• To offer an alternative to standard analytical techniques that struggle with complex term calculations.
• To demonstrate the simplicity and effectiveness of the proposed method.

Main Methods:

• The technique combines reproducing kernel functions with the shooting method.
• It provides a structured approach to discretize and solve fractional-order interface problems.
• Numerical examples are used to validate the method's performance.

Main Results:

• The proposed numerical technique successfully solves 1-D fractional-order interface problems.
• It effectively overcomes the difficulties associated with calculating complicated terms in analytical solutions.
• Numerical experiments confirm the technique's highlights and advantages.

Conclusions:

• The presented numerical technique is simple, effective, and clear for solving 1-D fractional-order interface problems.
• It offers a significant advantage over traditional analytical methods.
• The approach is well-suited for handling complex fractional calculus problems.