Integral operators are useful in real analysis, mathematical analysis, functional analysis and other subjects of mathematical approach. The goal of this paper is to study a unified integral operator via convexity. By using convexity and conditions of unified integral operators, bounds of these operators are obtained. Furthermore consequences of these results are discussed for fractional and conformable integral operators.
This paper is dedicated to Opial-type inequalities for arbitrary kernels using convex functions. These inequalities are further applied to a power function. Applications of the presented results are studied in fractional calculus via fractional integral operators by associating special kernels.
This work is to elaborate the Jeffery stagnation point flow towards a cylindrical surface with the homogenous–heterogeneous reactions, magnetic field, and heat generation effects. The heat transport process is delineated by the Cattaneo–Christov heat flux model in concert with the thermal stratification. The consequential PDEs are reduced to ODEs by carrying out a set of similarity transformations. These equations are solved numerically using the Runge–Kutta–Fehlberg technique along with the shooting proficiency. The involved parameters are analysed and provided by means of graphs. It is concluded that the Jeffery fluid velocity reflects inciting values for curvature parameter but the opposite aspects are recorded for the magnetic field parameter. Further, the Jeffery fluid concentration shows higher values via both the homogenous and heterogeneous reaction parameters. The obtained outcomes are validated with an existing work.
The main aim of this paper is to give refinement of bounds of fractional integral operators involving extended generalized Mittag-Leffler functions. A new definition, namely, strongly
α
,
m
-convex function is introduced to obtain improvements of bounds of fractional integral operators for convex,
m
-convex, and
α
,
m
-convex functions. The results of this paper will provide simultaneous generalizations as well as refinements of various published results.
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