Shahid Qaisar
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View article: Thermodynamic topology of black hole in Massive gravity with generalized Barrow modification of entropy
Thermodynamic topology of black hole in Massive gravity with generalized Barrow modification of entropy Open
The goal of our work is to explore the topology classifications of black holes in Massive gravity. We use Duan's ϕ-mapping theory to study the topology classes. This tool helps us to compute the integer numbers to characterize the topologi…
View article: A Fractional Version of Corrected Dual-Simpson's Type Inequality via s−convex Function with Applications
A Fractional Version of Corrected Dual-Simpson's Type Inequality via s−convex Function with Applications Open
Convexity plays a crucial role in mathematical analysis, offering profound insights into the behavior of functions and geometric shapes. Fractional integral operators generalize the classical concept of integration to non-integer orders. I…
View article: Error Bounds for Fractional Integral Inequalities with Applications
Error Bounds for Fractional Integral Inequalities with Applications Open
Fractional calculus has been a concept used to obtain new variants of some well-known integral inequalities. In this study, our main goal is to establish the new fractional Hermite–Hadamard, and Simpson’s type estimates by employing a diff…
View article: Fractional Simpson's type inequalities for twice differentiable convex functions with applications
Fractional Simpson's type inequalities for twice differentiable convex functions with applications Open
In this paper, we prove a new identity involving the second derivative of the function and Riemann-Liouville fractional integrals. The newly established identity is then used to establish some new Simpson’s type inequalities for twice diff…
View article: Generalizations of Simpson type inequality for (α,m)-convex functions
Generalizations of Simpson type inequality for (α,m)-convex functions Open
Several scholars are interested in fractional operators with integral inequalities. Due to its characteristics and wide range of applications in science, engineering fields, artificial intelligence and frac-tional inequalities should be em…
View article: Some Caputo-Fabrizio fractional integral inequalities with applications
Some Caputo-Fabrizio fractional integral inequalities with applications Open
Fractional calculus provides a significant generalization of classical concepts and overcomes the limitation of classical calculus in dealing with non-differentiability function. Implementing fractional operator to obtain new versions of c…
View article: On the P3-Coloring of Bipartite Graphs
On the P3-Coloring of Bipartite Graphs Open
The advancement in coloring schemes of graphs is expanding over time to solve emerging problems. Recently, a new form of coloring, namely P3-coloring, was introduced. A simple graph is called a P3-colorable graph if its vertices can be col…
View article: On the P3 Coloring of Graphs
On the P3 Coloring of Graphs Open
The vertex coloring of graphs is a well-known coloring of graphs. In this coloring, all of the vertices are assigned colors in such a way that no two adjacent vertices have the same color. We can call this type of coloring P2 coloring, whe…
View article: New inequalities via Caputo-Fabrizio integral operator with applications
New inequalities via Caputo-Fabrizio integral operator with applications Open
Fractional integral inequalities have become one of the most useful and expansive tools for the development of many fields of pure and applied mathematics over the past few years. Many authors have just recently introduced various generali…
View article: New developments in fractional integral inequalities via convexity with applications
New developments in fractional integral inequalities via convexity with applications Open
The main objective of this article is to build up a new integral equality related to Riemann Liouville fractional (RLF) operator. Based on this integral equality, we show numerous new inequalities for differentiable convex as well as conca…
View article: Certain fractional inequalities via the Caputo Fabrizio operator
Certain fractional inequalities via the Caputo Fabrizio operator Open
The Caputo Fabrizio fractional integral operator is one of the key concepts in fractional calculus. It is involved in many concrete and practical issues. In the present study, we have discussed some novel ideas to fractional Hermite-Hadama…
View article: New results on Hermite-Hadamard type inequalities via Caputo-Fabrizio fractional integral for s-convex function
New results on Hermite-Hadamard type inequalities via Caputo-Fabrizio fractional integral for s-convex function Open
The purpose of this article is to construction Hermite-Hadamard type inequalities via Caputo-Fabrizio fractional integral for s-convex function. The results are applied to fractional variations of Hermite-Hadamard type inequalities for dif…
View article: Some variants on Mercer's Hermite-Hadamard like inclusions of interval-valued functions for strong Kernel
Some variants on Mercer's Hermite-Hadamard like inclusions of interval-valued functions for strong Kernel Open
Using Atangana-Baleanu ($ AB $) fractional integral operators, we first establish some fractional Hermite-Hadamard-Mercer inclusions for interval-valued functions in this study. In this, some fresh developments of the Hermite-Hadamard ineq…
View article: Some Simpson’s Riemann–Liouville Fractional Integral Inequalities with Applications to Special Functions
Some Simpson’s Riemann–Liouville Fractional Integral Inequalities with Applications to Special Functions Open
Based on the Riemann–Liouville fractional integral, a new form of generalized Simpson-type inequalities in terms of the first derivative is discussed. Here, some more inequalities for convexity as well as concavity are established. We expe…
View article: Some Parameterized Quantum Simpson’s and Quantum Newton’s Integral Inequalities via Quantum Differentiable Convex Mappings
Some Parameterized Quantum Simpson’s and Quantum Newton’s Integral Inequalities via Quantum Differentiable Convex Mappings Open
In this work, two generalized quantum integral identities are proved by using some parameters. By utilizing these equalities, we present several parameterized quantum inequalities for convex mappings. These quantum inequalities generalize …
View article: On Some New Simpson’s Formula Type Inequalities for Convex Functions in Post-Quantum Calculus
On Some New Simpson’s Formula Type Inequalities for Convex Functions in Post-Quantum Calculus Open
In this work, we prove a new (p,q)-integral identity involving a (p,q)-derivative and (p,q)-integral. The newly established identity is then used to show some new Simpson’s formula type inequalities for (p,q)-differentiable convex function…
View article: Some Ostrowski type inequalities for mappings whose second derivatives are preinvex function via fractional integral operator
Some Ostrowski type inequalities for mappings whose second derivatives are preinvex function via fractional integral operator Open
The comprehension of inequalities in preinvexity is very important for studying fractional calculus and its effectiveness in many applied sciences. In this article, we develop and study of fractional integral inequalities whose second deri…
View article: <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"> <a:mi>k</a:mi> </a:math> -Fractional Variants of Hermite-Mercer-Type Inequalities via <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" id="M2"> <c:mi>s</c:mi> </c:math>-Convexity with Applications
k -Fractional Variants of Hermite-Mercer-Type Inequalities via s -Convexity with Applications Open
This article is aimed at studying novel generalizations of Hermite-Mercer-type inequalities within the Riemann-Liouville k -fractional integral operators by employing s -convex functions. Two new auxiliary results are derived to govern…
View article: New Inequalities of Simpson’s type for differentiable functions via generalized convex function
New Inequalities of Simpson’s type for differentiable functions via generalized convex function Open
This article presents some new inequalities of Simpson’s type for differentiable functions by using -convexity. Some results for concavity are also obtained. These new estimates improve on the previously known ones. Some applications for s…
View article: Hermite-Hadamard like inequalities for fractional integral operator via convexity and quasi-convexity with their applications
Hermite-Hadamard like inequalities for fractional integral operator via convexity and quasi-convexity with their applications Open
Since the supposed Hermite-Hadamard inequality for a convex function was discussed, its expansions, refinements, and variations, which are called Hermite-Hadamard type inequalities, have been widely explored. The main objective of this art…
View article: $Iq$-Hermite-Hadamard inclusions for the interval-valued functions of two variables
$Iq$-Hermite-Hadamard inclusions for the interval-valued functions of two variables Open
In this work, we introduce the concept of double quantum integrals for the interval-valued functions of two variables. We offer several new inclusions of the Hermite-Hadamard type for co-ordinated convex interval-valued functions using the…
View article: Hermite–Jensen–Mercer type inequalities for conformable integrals and related results
Hermite–Jensen–Mercer type inequalities for conformable integrals and related results Open
View article: Some results on integral inequalities via Riemann–Liouville fractional integrals
Some results on integral inequalities via Riemann–Liouville fractional integrals Open
View article: Some fractional integral inequalities of type Hermite–Hadamard through convexity
Some fractional integral inequalities of type Hermite–Hadamard through convexity Open
View article: More results on integral inequalities for strongly generalized ( ϕ , h , s ) $( \phi,h,s )$ -preinvex functions
More results on integral inequalities for strongly generalized ( ϕ , h , s ) $( \phi,h,s )$ -preinvex functions Open
The main goal of this research is to introduce a new form of generalized Hermite–Hadamard and Simpson type inequalities utilizing Riemann–Liouville fractional integral by a new class of preinvex functions which is known as strongly general…
View article: On Some Fractional Integral Inequalities of Hermite-Hadamard’s Type through Convexity
On Some Fractional Integral Inequalities of Hermite-Hadamard’s Type through Convexity Open
In this paper, we incorporate the notion of convex function and establish new integral inequalities of type Hermite–Hadamard via Riemann—Liouville fractional integrals. It is worth mentioning that the obtained inequalities generalize Hermi…
View article: New Hermite-Hadamard inequalities via fractional integrals, whose absolute values of second derivatives is P-convex
New Hermite-Hadamard inequalities via fractional integrals, whose absolute values of second derivatives is P-convex Open
In this research article, authors have established a general integral identity for Riemann-Liouville fractional integrals.Some new results related to the left-hand side of Hermite-Hadamard type integral inequalities utilizing this integral…
View article: New inequalities on Hermite-Hadamard utilizing fractional integrals
New inequalities on Hermite-Hadamard utilizing fractional integrals Open
In the present article, firstly authors have established an integral identity for Riemann-Liouville fractional integrals. Secondly, some Hermite-Hadamard type integral inequalities utilizing this integral identity are obtained and presente…
View article: On Hermite-Hadamard Type Inequalities for Functions Whose First Derivative Absolute Values are Convex and Concave
On Hermite-Hadamard Type Inequalities for Functions Whose First Derivative Absolute Values are Convex and Concave Open
In this paper, we derive general integral identity by establishing new Hermite-Hadamard type inequalities for functions whose absolute values of derivatives are convex and concave. Cor- responding error estimates for midpoint formula are a…
View article: NEW INTEGRAL INEQUALITIES THROUGH INVEXITY WITH APPLICATIONS
NEW INTEGRAL INEQUALITIES THROUGH INVEXITY WITH APPLICATIONS Open
In this paper, we obtain some inequalities of Simpson’s inequality type for functions whose derivatives absolute values are quasi-preinvex func-tion. Applications to some special means are considered. 1.