The goal of this article is to study the box dimension mixed Katugampola fractional integral two-dimensional continuous functions on $$[0,1]\times [0,1]$$ . We prove that having order $$(\alpha =(\alpha _1,\alpha _2);~ \alpha _1>0, _2>0)$$ still two. Moreover, results are also established for Hadamard integral. Our new improve existing studies. pose some open problems further research.

In this paper, we study the existence of positive solutions for a class of coupled integral boundary value problems of nonlinear semipositone Hadamard fractional differential equations Du(t) + λf(t, u(t), v(t)) = 0, Dv(t) + λg(t, u(t), v(t)) = 0, t ∈ (1, e), λ > 0, u(1) = v(1) = 0, 0 ≤ j ≤ n− 2, u(e) = μ ∫ e 1 v(s) ds s , v(e) = ν ∫ e

In this paper, the authors give a new identity for Hadamard fractional integrals. By using of this identity, the authors obtain new estimates on generalization of Hadamard, Ostrowski and Simpson type inequalities for (α,m)-GA-convex functions via Hadamard fractional integrals.

Abstract The main aim of this paper is establishing some new Volterra–Fredholm and Hermite–Hadamard-type fractional integral inequalities, which can be used as auxiliary tools in the study solutions to differential equations equations. Applications are also given explicate availability our results.

Fractional integral operators are useful tools for generalizing classical inequalities. Convex functions play very important role in the theory of mathematical This paper aims to investigate Hadamard type inequalities a generalized class namely strongly (α,h−m)-p-convex by using Riemann–Liouville fractional integrals. The results established this give refinements various well-known which have b...

AbstractIn this paper, we introduce a new class K(α, β) of uniformly convex functions defined by a certain fractional calculus operator. The class has interesting subclasses like β-uniformly starlike, βuniformly convex and β-uniformly pre-starlike functions. Properties like coefficient estimates, growth and distortion theorems, modified Hadamard product, inclusion property, extreme points, clos...

Given a function f ∈ C[0, 1] and some q ∈ (0, 1), we look at the approximation for the Hadamard finite-part integral = ∫ 1 0 x−q−1f(x)dx based on a piecewise linear interpolant for f at n equispaced nodes (i.e., the product trapezoidal rule). The main purpose of this paper is to give sufficient conditions for the sequence of approximations to converge against the correct value of the integral i...

In this paper we present fuzzy coupled fixed point results in the turf of complete b-metric spaces via nonlinear F-contraction; follow derive some interesting as byproducts. Eventually, apply our solving Volterra integral equations and Caputo-Hadamard type fractional differential equations.

In this paper, we give Hermite–Hadamard type inequalities of the Jensen–Mercer for Riemann–Liouville fractional integrals. We prove integral identities, and with help these identities some other eminent inequalities, such as Jensen, Hölder, power mean obtain bounds difference newly obtained inequalities.