Existence and uniqueness of weak and capacity solutions to fractional differential equations in fractional Musielak-Orlicz spaces

Key Points

• The research aims to establish the existence and uniqueness of weak and capacity solutions to fractional differential equations.
• Studied nonlinear fractional differential equation problems in fractional Musielak-Orlicz-Sobolev spaces.
• Used approximation techniques to create a sequence of converging approximated problems.
• Analyzed the convergence of solutions in the context of capacity.
• Demonstrated the existence of weak solutions under specified conditions.
• Established capacity solutions for the fractional differential equation problem.
• Illustrated practical applications confirming the relevance of the findings.