ARTICLE | doi:10.20944/preprints201711.0164.v2
Subject: Computer Science And Mathematics, Analysis Keywords: Fractional Calculus; Bessel-Struve Function; Fractional Kinetic Equations; Sumudu Transforms
Online: 27 November 2017 (05:23:54 CET)
In this paper, we pursue and investigate the solutions for fractional kinetic equations, involving Bessel-Struve function by means of their Sumudu transforms. In the process, one Important special case is then revealed, and analyzed. The results obtained in terms of Bessel-Struve function are rather general in nature and can easily construct various known and new fractional kinetic equations.
ARTICLE | doi:10.20944/preprints201810.0548.v1
Subject: Computer Science And Mathematics, Analysis Keywords: q-analogue of Sumudu transforms; q-analogue of hypergeometric functions; general class of q- polynomials; Fox’s H-function; basic analogue of I-function
Online: 24 October 2018 (05:37:37 CEST)
The prim objective of commenced article is to determine q-sumudu transforms of a product of unified family of q-polynomials with basic (or q-) analogue of fox’s H-function and q-analog of I-functions. Specialized cases of the leading outcome are further evaluated as q-sumudu transform of general class of q-polynomials and q-sumudu transforms of the basic analogues of Fox’s H-function and I-functions.
ARTICLE | doi:10.20944/preprints202012.0614.v1
Subject: Computer Science And Mathematics, Applied Mathematics Keywords: Gamma function, Sumudu transform, Laplace transform, convolution
Online: 24 December 2020 (09:45:36 CET)
Saif et al. (J. Math. Comput. Sci. 21 (2020) 127-135) considered modified Laplace transform and developed some of their certain properties and relations. Motivated by this work, in this paper, we define modified Sumudu transform and investigate many properties and relations including modified Sumudu transforms of the power function, sine, cosine, hyperbolic sine, hyperbolic cosine, exponential function, and function derivatives. Moreover, we attain two shifting properties and a scale preserving theorem for the modified Sumudu transform. We give modified inverse Sumudu transform and investigate some relations and examples. Furthermore, we show that the modified Sumudu transform is the theoretical dual transform to the modified Laplace transform.
ARTICLE | doi:10.20944/preprints202012.0626.v1
Subject: Computer Science And Mathematics, Applied Mathematics Keywords: Degenerate exponential function; degenerate gamma function; Sumudu transform; Laplace transform
Online: 24 December 2020 (13:52:29 CET)
Kim-Kim (Russ. J. Math. Phys. 2017, 24, 241-248) defined the degenerate Laplace transform and investigated some of their certain properties. Motivated by this study, in this paper, we introduce the degenerate Sumudu transform and establish some properties and relations. We derive degenerate Sumudu transforms of power functions, degenerate sine, degenerate cosine, degenerate hyperbolic sine, degenerate hyperbolic cosine, degenerate exponential function, and function derivatives. We also acquire a relationship between degenerate Sumudu transform and degenerate gamma function. Moreover, we investigate a scale preserving theorem for the degenerate Sumudu transform. Furthermore, we show that the degenerate Sumudu transform is the theoretical dual transform to the degenerate Laplace transform.
ARTICLE | doi:10.20944/preprints201806.0121.v1
Subject: Computer Science And Mathematics, Computer Science Keywords: fuzzy Sumudu transform; fuzzy linear differential equations; system of fuzzy differential equations
Online: 7 June 2018 (12:27:08 CEST)
In this paper, we employ fuzzy Sumudu transform for solving system of linear fuzzy differential equations with fuzzy constant coefficients. The system with fuzzy constant coefficients is interpreted under strongly generalized differentiability. For this purpose, new procedures for solving the system are proposed. A numerical example is carried out for solving system adapted from fuzzy radioactive decay model. Conclusion is drawn in the last section and some potential research directions are given.
ARTICLE | doi:10.20944/preprints201806.0095.v1
Subject: Computer Science And Mathematics, Applied Mathematics Keywords: dixon elliptic functions; non-zero modulus; sumudu transform; hankel determinants; continued fractions; Quasi C fractions
Online: 6 June 2018 (13:05:28 CEST)
Sumudu transform of the Dixon elliptic function with non zero modulus a ≠ 0 for arbitrary powers smN(x,a) ; N ≥ 1 ; smN(x,a)cm(x,a) ; N ≥ 0 and smN(x,a)cm2(x,a) ; N ≥ 0 is given by product of Quasi C fractions. Next by assuming denominators of Quasi C fraction to 1 and hence applying Heliermann correspondance relating formal power series (Maclaurin series of Dixon elliptic functions) and regular C fraction, Hankel determinants are calculated and showed by taking a = 0 gives the Hankel determinants of regular C fraction. The derived results were back tracked to the Laplace transform of sm(x,a) ; cm(x,a) and sm(x,a)cm(x,a).
ARTICLE | doi:10.20944/preprints201802.0150.v1
Subject: Computer Science And Mathematics, Discrete Mathematics And Combinatorics Keywords: discrete inverse Sumudu transform; Whittaker equation; Zettl equation; Gauss hypergeometric series and modified Struve function
Online: 24 February 2018 (07:31:17 CET)
Inverse Sumudu transform multiple shifting properties are used to design methodology for solving ordinary differential equations. Then algorithm applied to solve Whittaker and Zettl equations to get their new exact solutions and profiles which shown through Maple complex graphicals. Table of inverse Sumudu transforms for elementary functions given for supporting the differential equations solving using inverse Sumudu transform.