Box Dimension of Mixed Katugampola Fractional Integral of Two-Dimensional Continuous Functions [PDF]
arXiv, 2021 The goal of this article is to study the box dimension of the mixed Katugampola fractional integral of two-dimensional continuous functions on [0; 1]X[0; 1]. We prove that the box dimension of the mixed Katugampola fractional integral having fractional order (\alpha = (\alpha_1; \alpha_2); \alpha_1 > 0; \alpha_2 > 0) of two-dimensional continuous ...
Subhash Chandra, Syed Abbas
arxiv +3 more sources
Katugampola fractional integral and fractal dimension of bivariate functions [PDF]
arXiv, 2021 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
Saurabh Verma, P. Viswanathan
arxiv +3 more sources
Some Gruss-type Inequalities Using Generalized Katugampola Fractional Integral [PDF]
arXiv, 2019 The main objective of this paper is to obtain generalization of some Gruss-type inequalities in case of functional bounds by using a generalized Katugampola fractional integral.
Tariq A. Aljaaidi +1 more
arxiv +4 more sources
On Generalization of Some Inequalities of Chebyshevs Functional Using Generalized Katugampola Fractional Integral [PDF]
arXiv, 2019 In this paper we obtain a generalization of some integral inequalities related to Chebyshev`s functional by using a generalized Katugampola fractional integral.
Tariq A. Aljaaidi +1 more
arxiv +3 more sources
New Approach To A Generalized Fractional Integral [PDF]
Appl. Math. Comput. Vol 218, Issue 3, 1 October 2011, p. 860-865, 2010 The paper presents a new formula for the fractional integration, which generalizes the Riemann-Liouville and Hadamard fractional integrals into a single form, which when a parameter fixed at different values, produces the above integrals as special cases.
arxiv +1 more source
Hermite-Hadamard and Hermite-Hadamard-Fejér type Inequalities for Generalized Fractional Integrals [PDF]
Journal of Mathematical Analysis and Applications 446 (2017), pp.
1274-1291, 2016 In this paper we obtain the Hermite-Hadamard and Hermite-Hadamard-Fej\'er type inequalities for fractional integrals which generalize the two familiar fractional integrals namely, the Riemann-Liouville and the Hadamard fractional integrals into a single form.
arxiv +1 more source
Mellin Transforms of the Generalized Fractional Integrals and Derivatives [PDF]
Applied Mathematics and Computation 257 (2015) 566-580, 2011 We obtain the Mellin transforms of the generalized fractional integrals and derivatives that generalize the Riemann-Liouville and the Hadamard fractional integrals and derivatives. We also obtain interesting results, which combine generalized $\delta_{r,m}$ operators with generalized Stirling numbers and Lah numbers.
arxiv +1 more source
Katugampola Fractional Calculus With Generalized $k-$Wright Function [PDF]
arXiv, 2019 In this article, we presented some properties of the Katugampola fractional integrals and derivatives. Also we studied the fractional calculus properties involving Katugampola Fractional integrals and derivatives of generalized $k-$Wright function $_{n}\Phi_{m}^{k}(z).$\\[2mm]
arxiv
Fractal dimension of Katugampola fractional integral of vector-valued functions [PDF]
, 2021 Megha Pandey, Tanmoy Som, Saurabh Verma
openalex +1 more source
New fractional integral unifying six existing fractional integrals [PDF]
arXiv, 2016 In this paper we introduce a new fractional integral that generalizes six existing fractional integrals, namely, Riemann-Liouville, Hadamard, Erd\'elyi-Kober, Katugampola, Weyl and Liouville fractional integrals in to one form. Such a generalization takes the form \[ \left({}^{\rho}\mathcal{I}^{\alpha, \beta}_{a+;\eta, \kappa}f\right)(x)=\frac{\rho ...
arxiv