The analytical solution of Van der Pol and Lienard differential equations within conformable fractional operator by retarded integral inequalities

Abstract

In this study we introduced and tested retarded conformable fractional integral inequalities utilizing non-integer order derivatives and integrals. In line with this purpose, we used the Katugampola type conformable fractional calculus which has several practical properties. These inequalities generalize some famous integral inequalities which provide explicit bounds on unknown functions. The results provided here had been implemented to the global existence of solutions to the conformable fractional differential equations with time delay.

Keywords

• global existence
• retarded integral inequalities
• conformable fractional van der pol differential equation
• conformable fractional liènard differential equation
• 26a42
• 26a51
• 26d15
• 26a33