Abstract
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.
Highlights
Being important tools in the analysis of differential equations, integral equations and integro-differential equations, a number of generalizations of Gronwall inequality and their utilizations have greatly attracted the interests of several mathematicians
The results provided here had been implemented to the global existence of solutions to the conformable fractional differential equations with time delay
We presented a retarded conformable fractional integral inequalities using the Katugampola conformable fractional calculus
Summary
Being important tools in the analysis of differential equations, integral equations and integro-differential equations, a number of generalizations of Gronwall inequality and their utilizations have greatly attracted the interests of several mathematicians. We refer the readers to [8]-[12] and references therein This new idea was quickly generalized by Katugampola [13], whose definition forms the basis for this work and is referred to here as the Katugampola derivative (Dα will be referred to the Katugampola derivative). This definition has several practical properties which are summarized below.
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