766 citations · 1.8k across the 10 of their papers we have counts for
12 papers
On the Gap Structure of Generalized Stirling Numbers
Jianru Shen, Udita N. Katugampola
Katugampola's 2015 study of generalized fractional differential operators produced triangular arrays of integer coefficients indexed by a fractional order r and by dimensions n and…
Finding Eigenvectors: Fast and Nontraditional Approach
Udita N. Katugampola
Diagonalizing a matrix , that is finding two matrices and such that with being a diagonal matrix needs two steps: first find the eigenvalues and then…
New fractional integral unifying six existing fractional integrals
Udita N. Katugampola
In this paper we introduce a new fractional integral that generalizes six existing fractional integrals, namely, Riemann-Liouville, Hadamard, Erdélyi-Kober, Katugampola, Weyl and L…
Hermite-Hadamard and Hermite-Hadamard-Fejér type Inequalities for Generalized Fractional Integrals
Hua Chen, Udita N. Katugampola
In this paper we obtain the Hermite-Hadamard and Hermite-Hadamard-Fejér type inequalities for fractional integrals which generalize the two familiar fractional integrals namely, th…
Geometric Approach to the integral
Udita N. Katugampola
We give a geometric proof of the evaluation of the integral which is normally done using a rather ad hoc approach.
Applications of fractional calculus in solving Abel-type integral equations: Surface-volume reaction problem
Ryan M. Evans, Udita N. Katugampola, David A. Edwards
In this paper we consider a class of partial integro-differential equations of fractional order, motivated by an equation which arises as a result of modeling surface-volume reacti…
A New Fractional Derivative with Classical Properties
Udita N. Katugampola
We introduce a new fractional derivative which obeys classical properties including: linearity, product rule, quotient rule, power rule, chain rule, vanishing derivatives for const…
Existence and Uniqueness results for a class of Generalized Fractional Differential Equations
Udita N. Katugampola
The author (Bull. Math. Anal. App. 6(4)(2014):1-15), introduced a new fractional derivative, \[{}^ρ\mathcal{D}_a^αf (x) = \frac{ρ^{α-n+1}}{Γ({n-α})} \, \bigg(x^{1-ρ} \,\frac{d}{dx}…
Mellin Transforms of the Generalized Fractional Integrals and Derivatives
Udita N. Katugampola
We obtain the Mellin transforms of the generalized fractional integrals and derivatives that generalize the Riemann-Liouville and the Hadamard fractional integrals and derivatives.…
A New Approach to Generalized Fractional Derivatives
Udita N. Katugampola
The author \mbox{(Appl. Math. Comput. 218(3):860-865, 2011)} introduced a new fractional integral operator given by, \[ \big({}^ρ\mathcal{I}^α_{a+}f\big)(x) = \frac{ρ^{1- α}}{Γ(α)}…
A New Technique for Text Data Compression
Udita N. Katugampola
In this paper we use ternary representation of numbers for compressing text data. We use a binary map for ternary digits and introduce a way to use the binary 11-pair, which has ne…
New Approach To A Generalized Fractional Integral
Udita N. Katugampola
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 paramete…