Abstract
The present work investigates the applicability and effectiveness of the generalized Riemann-Liouville fractional integral operator integral method to obtain new Minkowski, Gr\"{u}ss type and several other associated dynamic variants on an arbitrary time scale, which are communicated as a combination of delta and fractional integrals. These inequalities extend some dynamic variants on time scales, and tie together and expand some integral inequalities. The present method is efficient, reliable, and it can be used as an alternative to establishing new solutions for different types of fractional differential equations applied in mathematical physics.
Highlights
Fractional calculus has been comprehensively utilized in several instances, but the concept has been popularized and implemented in numerous disciplines of science, technology and engineering as a mathematical model
Numerous distinguished generalized fractional integral operators consist of the Hadamard operator, Erdlelyi-Kober operators, the Saigo operator, the Gaussian hypergeometric operator, the Marichev-Saigo-Maeda fractional integral operator, and so on.; out of the ones, the Riemann-Liouville fractional integral operator has been extensively utilized by researchers in theory as well as applications
We study the dynamic variants of corresponding generalized fractional-order on time scales
Summary
Saima Rashid 1, Muhammad Aslam Noor 2, Kottakkaran Sooppy Nisar 3*, Dumitru Baleanu 4,5,6 and Gauhar Rahman 7. The present work investigates the applicability and effectiveness of the generalized Riemann-Liouville fractional integral operator integral method to obtain new Minkowski, Grüss type and several other associated dynamic variants on an arbitrary time scale, which are communicated as a combination of delta and fractional integrals. These inequalities extend some dynamic variants on time scales, and tie together and expand some integral inequalities. The present method is efficient, reliable, and it can be used as an alternative to establishing new solutions for different types of fractional differential equations applied in mathematical physics
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