Katugampola Fractional Integrals Research Articles

Boundary value problems for Hilfer fractional differential equations with Katugampola fractional integral and anti-periodic conditions

The purpose of this paper is to investigate the existence and uniqueness of solutions for a new class of nonlinear fractional differential equations involving Hilfer fractional operator with fractional integral boundary conditions. Our analysis relies on classical fixed point theorems and the Boyd-Wong nonlinear contraction. At the end, an illustrative example is presented. The boundary conditions introduced in this work are of quite general nature and can be reduce to many special cases by fixing the parameters involved in the conditions.

Katugampola Fractional Calculus With Generalized k−Wright Function

In this article, we present some properties of the Katugampola fractional integrals and derivatives. Also, we study the fractional calculus properties involving Katugampola Fractional integrals and derivatives of generalized k−Wright function nΦkm(z).

Katugampola Fractional Integral and Fractal Dimension of Bivariate Functions

The subject of this note is the mixed Katugampola fractional integral of a bivariate function defined on a rectangular region in the Cartesian plane. This is a natural extension of the Katugampola fractional integral of a univariate function—a concept well-received in the recent literature on fractional calculus and its applications. It is shown that the mixed Katugampola fractional integral of a prescribed bivariate function preserves properties such as boundedness, continuity and bounded variation of the function. Furthermore, we estimate fractal dimension of the graph of the mixed Katugampola integral of a continuous bivariate function. Some examples for bivariate functions that are not of bounded variation but with graphs having box dimension 2 are constructed. The findings in the current note may be viewed as a sequel to our work reported in [Appl. Math. Comp., 339, 2018, pp. 220–230].

Generalized fractional Hadamard type inequalities for \(Q_s\)-class functions of the second kind

New Hadamard type inequalities for a class of \(s\)-Godunova-Levin functions of the second kind for fractional integrals are obtained. These new estimates extend and generalize some existing results for the \(Q\)-class and \(P\)-class functions. The generalized case for the Katugampola fractional integrals are also given.

Fractal dimension of graph of Katugampola fractional integral and some general characterizations

Fractal dimension of graph of Katugampola fractional integral and some general characterizations

Hermite-Hadamard-Fejér type inequalities for co-ordinated harmonically convex functions via Katugampola fractional integrals

The aim of this paper is to establish the Hermite-Hadamard-Fejér type inequalities for co-ordinated harmonically convex functions via Katugampola fractional integral. We provide Hermite-Hadamard-Fejér inequalities for harmonically convex functions via Katugampola fractional integral in one dimension.

Analytical properties of (k, s)-Riemann–Liouville fractional integral and its fractal dimension

A prominent study problem that gained unbearable attraction is to calculate the fractal dimensions of the graph of a fractional integral of a function. The present article is a study about the analytical properties, such as boundedness, continuity and bounded variation of (k, s)-Riemann–Liouville fractional integral of a function, which generalizes the Katugampola fractional integral. Further, we investigate the Hausdorff dimension and box dimension of the graph of (k, s)-Riemann–Liouville fractional integral of a continuous function defined on a compact interval [a, b] and derived the conclusion that these two dimensions are 1. Also we establish a relation between the order of the fractional integral and upper box dimension.

New trapezium type inequalities of coordinated distance-disturbed convex type functions of higher orders via extended Katugampola fractional integrals

In this paper we establish some new results on trapezium type inequalities of coordinated distance-disturbed (ell _{1},h_{1})–(ell _{2},h_{2})-convex functions of higher orders (sigma _{1},sigma _{2}) by using the Katugampola (k_{1},k_{2})-fractional integrals. As special cases of our general results, we recapture some earlier proved results.

On the weighted fractional integral inequalities for Chebyshev functionals

The goal of this present paper is to study some new inequalities for a class of differentiable functions connected with Chebyshev’s functionals by utilizing a fractional generalized weighted fractional integral involving another function mathcal{G} in the kernel. Also, we present weighted fractional integral inequalities for the weighted and extended Chebyshev’s functionals. One can easily investigate some new inequalities involving all other type weighted fractional integrals associated with Chebyshev’s functionals with certain choices of omega (theta ) and mathcal{G}(theta ) as discussed in the literature. Furthermore, the obtained weighted fractional integral inequalities will cover the inequalities for all other type fractional integrals such as Katugampola fractional integrals, generalized Riemann–Liouville fractional integrals, conformable fractional integrals and Hadamard fractional integrals associated with Chebyshev’s functionals with certain choices of omega (theta ) and mathcal{G}(theta ).

SIMPSON’S TYPE INEQUALITIES VIA THE KATUGAMPOLA FRACTIONAL INTEGRALS FOR s-CONVEX FUNCTIONS

In this paper, we introduce some Simpson’s type integral inequalities via the Katugampola fractional integrals for functions whose first derivatives at certain powers are s-convex (in the second sense). The Katugampola fractional integrals are generalizations of the Riemann–Liouville and Hadamard fractional integrals. Hence, our results generalize some results in the literature related to the Riemann–Liouville fractional integrals. Results related to the Hadamard fractional integrals could also be derived from our results.

Estimates of upper bound for differentiable mappings related to Katugampola fractional integrals and $ p $-convex mappings

We use the definition of a fractional integral operators, recently introduced by Katugampola, to establish a parameterized identity associated with differentiable mappings. The identity is then used to derive the estimates of upper bound for mappings whose first derivatives absolute values are $ p $-convex mappings. Four examples are also provided to illustrate the obtained results.

Generalized Fractional Inequalities of the Hermite–Hadamard Type for Convex Stochastic Processes

Abstract A generalization of the Hermite–Hadamard (HH) inequality for a positive convex stochastic process, by means of a newly proposed fractional integral operator, is hereby established. Results involving the Riemann– Liouville, Hadamard, Erdélyi–Kober, Katugampola, Weyl and Liouville fractional integrals are deduced as particular cases of our main result. In addition, we also apply some known HH results to obtain some estimates for the expectations of integrals of convex and p-convex stochastic processes. As a side note, we also pointed out a mistake in the main result of the paper [Hermite–Hadamard type inequalities, convex stochastic processes and Katugampola fractional integral, Revista Integración, temas de matemáticas 36 (2018), no. 2, 133–149]. We anticipate that the idea employed herein will inspire further research in this direction.

On the weighted fractional P\xf3lya\u2013Szeg\xf6 and Chebyshev-types integral inequalities concerning another function

The primary objective of this present paper is to establish certain new weighted fractional Pólya–Szegö and Chebyshev type integral inequalities by employing the generalized weighted fractional integral involving another function Ψ in the kernel. The inequalities presented in this paper cover some new inequalities involving all other type weighted fractional integrals by applying certain conditions on omega (theta ) and Psi (theta ). Also, the Pólya–Szegö and Chebyshev type integral inequalities for all other type fractional integrals, such as the Katugampola fractional integrals, generalized Riemann–Liouville fractional integral, conformable fractional integral, and Hadamard fractional integral, are the special cases of our main results with certain choices of omega (theta ) and Psi (theta ). Additionally, examples of constructing bounded functions are also presented in the paper.

Some New Tempered Fractional Pólya-Szegö and Chebyshev-Type Inequalities with Respect to Another Function

In this present article, we establish certain new Pólya–Szegö-type tempered fractional integral inequalities by considering the generalized tempered fractional integral concerning another functionΨin the kernel. We then prove certain new Chebyshev-type tempered fractional integral inequalities for the said operator with the help of newly established Pólya–Szegö-type tempered fractional integral inequalities. Also, some new particular cases in the sense of classical tempered fractional integrals are discussed. Additionally, examples of constructing bounded functions are considered. Furthermore, one can easily form new inequalities for Katugampola fractional integrals, generalized Riemann–Liouville fractional integral concerning another functionΨin the kernel, and generalized fractional conformable integral by applying different conditions.

New integral inequalities of Hermite–Hadamard type via the Katugampola fractional integrals for strongly $$\eta$$-quasiconvex functions

In this paper, we introduce new integral inequalities of the Hermite–Hadamard type for strongly $$\eta$$ -quasiconvex functions via the Katugampola fractional integrals. Some results in the literature are particular cases of some of our results.

Bounds for the Remainder in Simpson’s Inequality vian-Polynomial Convex Functions of Higher Order Using Katugampola Fractional Integrals

The goal of this paper is to derive some new variants of Simpson’s inequality using the class ofn-polynomial convex functions of higher order. To obtain the main results of the paper, we first derive a new generalized fractional integral identity utilizing the concepts of Katugampola fractional integrals. This new fractional integral identity will serve as an auxiliary result in the development of the main results of this paper.

On Inequalities for S-Convex Function Based on Katugampola Fractional Integral

The subject of integral inequalities has been considered and studied by many mathematical scholars. Based on Katugampola fractional integrals in this article, authors discuss s-function and obtain some inequalities.

Quasi-Convex Functions and Their Inequalities Based on Fractional Integrals

In the article, on the basis of Katugampola fractional integrals and with , the quasi-convex function is discussed and a few inequalities are derived.

SOME REMARKS ON FRACTIONAL INTEGRAL OF ONE-DIMENSIONAL CONTINUOUS FUNCTIONS

In this paper, we make research on Katugampola and Hadamard fractional integral of one-dimensional continuous functions on [Formula: see text]. We proved that Katugampola fractional integral of bounded and continuous function still is bounded and continuous. Box dimension of any positive order Hadamard fractional integral of one-dimensional continuous functions is one.

Hermite-Hadamard’s mid-point type inequalities for generalized fractional integrals

Some Hermite-Hadamard’s mid-point type inequalities related to Katugampola fractional integrals are obtained where the first derivative of considered mappings is Lipschitzian or convex. Also some mid-point type inequalities are given for Lipschitzian mappings, with the aim of generalizing the results presented in previous works. Finally, some generalized inequalities in connection with special means are provided.