Exploring variable order fractional initial value problems: Existence results and weak topology insights

Key Points

• Weak solutions exist for initial value problems involving variable order fractional derivatives, highlighting their applicability.
• Utilizing Krasnoselskii's fixed point theorem under weak topology, the study establishes necessary conditions for these solutions.
• Illustrative examples demonstrate the practical implications of these theoretical findings in mathematics.
• This analysis may enhance understanding of complex systems modeled by fractional calculus in various scientific fields.