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. examines the construction of solutions equations are associated varying delay proportional to independent variable using a hybrid Sumudu transform method. considers Caputo derivatives orders their applications in Nuclear Physics. The application indicates have useful as tools modelling many anomalous phenomena nature theory complex systems.