There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Fractional Differential Equations

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Aufgaben und Lehrsätze aus der Analysis

Convex functions and their applications

In this article, we define a new fractional technique which is known as generalized proportional fractional (GPF) integral in the sense of another function Ψ . The authors prove several inequalities for newly defined GPF-integral with respect to another function Ψ . Our consequences will give noted outcomes for a suitable variation to the GPF-integral in the sense of another function Ψ and the proportionality index ς . Furthermore, we present the application of the novel operator with several integral inequalities. A few new properties are exhibited, and the numerical approximation of these new operators is introduced with certain utilities to real-world problems.

https://www.mdpi.com/2227-7390/7/12/1225/pdf

Inequalities by Means of Generalized Proportional Fractional Integral Operators with Respect to Another Function

In this study, new and general variants have been obtained on Chebyshev’s inequality, which is quite old in inequality theory but also a useful and effective type of inequality. The main findings obtained by using integrable functions and generalized fractional integral operators have generalized many existing results as well as iterating the Chebyshev inequality in special cases.

New General Variants of Chebyshev Type Inequalities via Generalized Fractional Integral Operators

Some new results related to the left-hand side of the Hermite-Hadamard type inequalities for the class of functions whose second derivatives at certain powers are s-convex functions in the second sense are obtained. Also, some applications to special means of real numbers are provided. MSC:26A51, 26D15.

/pdf/on-some-inequalities-for-s-convex-functions-and-applications-14oayb60yr.pdf

On some inequalities for s-convex functions and applications

The coronavirus still an epidemic in most countries of the world and put the people in danger with so many infected cases and death. Considering the third wave of corona virus infection and to determine the peak of the infection curve, we suggest a new mathematical model with reported cases from March 06

Results in Physics

In this article, Hadamard-type inequalities for product of s-convex in the second sense on the co-ordinates in a rectangle from the plane are established.

/pdf/on-some-hadamard-type-inequalities-for-product-of-two-s-1kdt0h2in3.pdf

On some Hadamard-type inequalities for product of two s-convex functions on the co-ordinates

In this paper some new inequalities of Simpson-type are established for the classes of functions whose derivatives of absolute values are convex functions via Riemann-Liouville integrals. Also, by special selections of n;we give some reduced results.

/pdf/simpson-type-integral-inequalities-for-convex-functions-via-2n3gw4gc9w.pdf

Ahmet Ocak Akdemir

Papers

New General Variants of Chebyshev Type Inequalities via Generalized Fractional Integral Operators

On some inequalities for s-convex functions and applications

Results in Physics

On some Hadamard-type inequalities for product of two s-convex functions on the co-ordinates

Simpson type integral inequalities for convex functions via riemann-liouville integrals