Search

Fractional inequalities play a crucial role in building mathematical mechanisms and their related solution functions across the majority of practical science domains. A variety of mathematical disciplines are significantly impacted by convexity as well. In this article, we describe and verify many new fractional inequalities using a thorough kind of Riemann–Liouville integral and the convexity criterion of the functions. Our approach for dealing with fractional integral inequalities is clear and easy to use, and the current study is a new addition to the literature. Additionally, it is simple to observe that all the inequalities produced are extensive and may be broken down into several and different inequalities that were previously in the literature. [ABSTRACT FROM AUTHOR]

This paper is devoted to proving some new fractional inequalities via recent generalized fractional operators. These inequalities are in the Hermite–Hadamard and Minkowski settings. Many previously documented inequalities may clearly be deduced as specific examples from our findings. Moreover, we give some comparative remarks to show the advantage and novelty of the obtained results. [ABSTRACT FROM AUTHOR]

In this work, the elliptic 2 × 2 cooperative systems involving fractional Laplace operators are studied. Due to the nonlocality of the fractional Laplace operator, we reformulate the problem into a local problem by an extension problem. Then, the existence and uniqueness of the weak solution for these systems are proved. Hence, the existence and optimality conditions are deduced. [ABSTRACT FROM AUTHOR]