Gronwall type inequality on generalized fractional conformable integral operators

• DOI: 10.1515/anly-2022-1105
• Publication Date: 2023-11-29T11:23:27Z
• Authors: Vandana Palsaniya; Ekta Mittal; Sunil Joshi; D. L. Suthar
• Keywords: Conformable matrix; Gronwall's inequality

Abstract In 2015, Abdeljawad defined the conformable fractional derivative (Grunwald–Letnikov technique) to iterate integral of order <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mn>0</m:mn> <m:mo>&lt;</m:mo> <m:mi>α</m:mi> <m:mo>≤</m:mo> <m:mn>1</m:mn> </m:mrow> </m:math> {0&lt;\alpha\leq{1}} (Riemann approach), yielding Hadamard integrals when <m:mo>=</m:mo> {\alpha=0} . The Gronwall type inequality for generalized operators unifying Riemann–Liouville and is obtained in this study. We use show how initial conditions affect solution differential equations with derivatives. More features are established, as well solutions value problems several new weighted spaces functions.