On an initial boundary value problem for fractional pseudo-parabolic equation with conformable derivative

Area of Science:

• Mathematical analysis
• Partial differential equations
• Fractional calculus

Background:

• Pseudo-parabolic equations present complex behavior.
• Conformable derivatives offer a novel approach to modeling.
• Understanding global solutions and regularity is crucial for applications.

Purpose of the Study:

• To analyze the initial boundary value problem for pseudo-parabolic equations with conformable derivatives.
• To establish the existence of global solutions and investigate their regularity.
• To explore the convergence properties of these solutions under specific conditions.

Main Methods:

• Banach fixed point theorem for existence and uniqueness.
• Sobolev embedding theorems for regularity analysis.
• Specialized techniques for evaluating generalized integral convergence.

Main Results:

• Existence of global solutions for the pseudo-parabolic equation with conformable derivative.
• Proof of convergence from pseudo-parabolic to parabolic equation solutions.
• Analysis of solution convergence as the fractional derivative order approaches 1.

Conclusions:

• The study provides a rigorous mathematical framework for pseudo-parabolic equations with conformable derivatives.
• The findings contribute to the understanding of fractional calculus applications in differential equations.
• This work offers insights into the behavior of solutions as fractional orders tend towards integer orders.