On more general inequalities for weighted generalized proportional Hadamard fractional integral operator with applications

Zhou, Shuang-Shuang; Rashid, Saima; Set, Erhan; Ahmad, Abdulaziz Garba; Hamed, Y. S.

doi:10.3934/math.2021532

Cited by 5 publications

(1 citation statement)

References 61 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In perspective on the broad utilization of such frameworks, numerous scientists went to the examination of the hypothetical parts of fractional differential conditions. Specifically, there was unique consideration regarding demonstrating the integral inequalities for fractional systems enhanced with an assortment of classical and non-classical (nonlocal) operators with the guide of advance strategies for functional investigation, see [5,6,7,8,9,10,11,12,13,14,15,16,17,18,59,60,61,62,63,64,65]. Fractional integral inequalities involving convex functions played a significant role in the mathematical analysis due to their prominent features and convenient characterizations.…”

Section: Introductionmentioning

confidence: 99%

Some new generalizations for exponentially (s, m)-preinvex functions considering generalized fractional integral operators

Safdar

Attique

2021

Punjab Univ. j. math.

View full text Add to dashboard Cite

The generalized fractional integral has been one of the most useful operators for modelling non-local behaviors by fractional differential equations. It is considered, for several integral inequalities by introducing the concept of exponentially (s, m)-preinvexity. These variants derived via an extended Mittag-Leffler function based on boundedness, continuity and Hermite-Hadamard type inequalities. The consequences associated with fractional integral operators are more general and also present the results for convexity theory. Moreover, we point out that the variants are useful in solving the problems of science, engineering and technology where the Mittag-Leffler function occurs naturally.

show abstract

Section: Introductionmentioning

confidence: 99%

Some new generalizations for exponentially (s, m)-preinvex functions considering generalized fractional integral operators

Safdar

Attique

2021

Punjab Univ. j. math.

View full text Add to dashboard Cite

show abstract

New midpoint-type inequalities in the context of the proportional Caputo-hybrid operator

Demir,

Tunç

2024

J Inequal Appl

View full text Add to dashboard Cite

Fractional calculus is a crucial foundation in mathematics and applied sciences, serving as an extremely valuable tool. Besides, the new hybrid fractional operator, which combines proportional and Caputo operators, offers better applications in numerous fields of mathematics and computer sciences. Due to its wide range of applications, we focus on the proportional Caputo-hybrid operator in this research article. Firstly, we begin by establishing a novel identity for this operator. Then, based on the newfound identity, we establish some integral inequalities that are relevant to the left-hand side of Hermite–Hadamard-type inequalities for the proportional Caputo-hybrid operator. Furthermore, we show how the results improve upon and refine many previous findings in the setting of integral inequalities. Later, we present specific examples together with their related graphs to offer a better understanding of the newly obtained inequalities. Our results not only extend previous studies but also provide valuable viewpoints and methods for tackling a wide range of mathematical and scientific problems.

show abstract

Novel Integral Transform Treating Some Ψ-Fractional Derivative Equations

Chamekh,

Latrach,

Elzaki

2024

Acta Mechanica Et Automatica

View full text Add to dashboard Cite

The paper deals with a new integral transformation method called Ψ-Elzaki transform (PETM) in order to analyze some Ψ-fractional differential equations. The proposed method uses a modification of the Elzaki transform that is well adapted to deal with Ψ-fractional operators. To solve the nonlinear Ψ-fractional differential equations, we combine the PETM by an iterative method to overcome this nonlinearity. To validate the accuracy and efficiency of this approach, we compare the results of the discussed numerical examples with the exact solutions.

show abstract

On more general inequalities for weighted generalized proportional Hadamard fractional integral operator with applications

Cited by 5 publications

References 61 publications

Some new generalizations for exponentially (s, m)-preinvex functions considering generalized fractional integral operators

Some new generalizations for exponentially (s, m)-preinvex functions considering generalized fractional integral operators

New midpoint-type inequalities in the context of the proportional Caputo-hybrid operator

Novel Integral Transform Treating Some Ψ-Fractional Derivative Equations

Contact Info

Product

Resources

About