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

Usta Fuat, Sarıkaya Mehmet Zeki

Demonstratio Mathematica

2019

Vol. 52, nr 1

204--212

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.

Explicit bounds on some retarded integral inequalities

Pachpatte B. G.

Fasciculi Mathematici

2005

Nr 35

85-98

In this paper we establish some new retarded integral inequalities which provide explicit bounds on unknown functions. Applications are also given to illustrate the usefulness of one of our results.