Approximate analytical solutions and applications of pantograph-type equations with Caputo derivative and variable orders

This study presents an efficient method that is suitable for differential equations, both with integer-order and fractional derivatives. This study examines the construction of solutions of fractional differential equations that are associated with varying delay proportional to the independent variable using a hybrid of Sumudu transform method. This study considers differential equations with Caputo derivatives of fractional variable orders and their applications in Nuclear Physics. The application indicates that fractional differential equations that have varying delay proportional to the independent variable are useful as tools for the modelling of many anomalous phenomena in nature and in the theory of complex systems.