A note on fractional Sumudu transform

We propose a new definition of a fractional-order Sumudu transform for fractional differentiable functions. In the development of the definition we use fractional analysis based on the modified Riemann-Liouville derivative that we name the fractional Sumudu transform. We also established a relationship between fractional Laplace and Sumudu duality with complex inversion formula for fractional Sumudu transform and apply new definition to solve fractional differential equations

On some applications of a new integral transform.

In this work a new integral transform, namely Sumudu transform was applied to solve linear ordinary differential equation with and without constant coefficients having convolution terms. In particular we apply Sumudu transform technique to solve Spring-Mass systems, Population Growth and financial problem

PENERAPAN TRANSFORMASI SUMUDU PADA PERSAMAAN KONSENTRASI OKSIGEN TERLARUT

ABSTRAKPenelitian ini membahas mengenai penerapan transformasi Sumudu pada persamaan konsentrasi oksigen terlarut (DO) dengan reaksi kebutuhan oksigen biologi (BOD) orde satu dan orde 3/2. Transformasi Sumudu merupakan salah satu transformasi integral yang diperkenalkan oleh Watugala. Transformasi Sumudu memiliki beberapa sifat dasar yang identik dengan transformasi Laplace, yaitu sifat linearitas, konvolusi, turunan dan Laplace-Sumudu duality (LSD). DO merupakan parameter kunci untuk melihat kualitas air sungai. Pemodelan kualitas air sungai pertama kali dikembangkan oleh Streeter dan Phelps, yang menggambarkan perkiraan penurunan DO di sungai akibat dari BOD, dan dimodelkan dengan persamaan diferensial biasa orde satu. Dari penelitian ini didapatkan solusi untuk persamaan konsentrasi DO dengan reaksi BOD orde satu dan orde 3/2 menggunakan transformasi Sumudu. Untuk persamaan konsentrasi DO dengan reaksi BOD orde 3/2, solusi yang didapat tidak mengandung konstanta laju reaksi orde 3/2. Berdasarkan hasil uji data, didapatkan bahwa kandungan BOD pada sungai Babon dan Passaic semakin menurun dan untuk kandungan DO semakin meningkat seiring berjalannya waktu. Hal ini menunjukkan bahwa kualitas air pada sungai Babon dan sungai Passaic semakin membaik.Kata kunci: transformasi Sumudu, DO, BOD.ABSTRACTThis study discusses about the application of Sumudu transform to the dissolved oxygen (DO) concentration equation with the reaction of biological oxygen demand (BOD) of first order and 3/2 order. The Sumudu transform is one of the integral transform introduced by Watugala. The Sumudu transform has several basic properties that are identical to Laplace transform; they are linearity, convolution, derivative and Laplace-Sumudu duality (LSD). DO is a key parameter to see the quality of river water. The water quality modeling of the river was first developed by Streeter and Phelps, which illustrates the approximate decrease of DO in rivers as a result of BOD, and modelled by the differential equation of first order. From this research that was found a solution for the DO concentration equation with BOD reaction of first order and 3/2 order using Sumudu transform. For the DO concentration equation with BOD reaction of 3/2 order, the solution found does not contain the rate reaction constant of 3/2 order. Based on the results of the data test, it was found that the BOD content in the Babon River and Passaic River is decreasing and the DO content is increasing with time. This indicates that the water quality in the Babon River and the Passaic River is getting better.Keywords: Sumudu transform, DO, BOD

New integral transform: Shehu transform a generalization of Sumudu and Laplace transform for solving differential equations

In this paper, we introduce a Laplace-type integral transform called the Shehu transform which is a generalization of the Laplace and the Sumudu integral transforms for solving differential equations in the time domain. The proposed integral transform is successfully derived from the classical Fourier integral transform and is applied to both ordinary and partial differential equations to show its simplicity, efficiency, and the high accuracy

On the applications of Laplace and Sumudu transforms.

In this paper, we study the properties of Sumudu transform and relationship between Laplace and Sumudu transforms. Further, we also provide an example of the double Sumudu transform in order to solve the wave equation in one dimension which is having singularity at initial conditions

A note on the comparison between laplace and Sumudu transforms.

In this paper, we discuss the existence of double Sumudu transform and study relationships between Laplace and Sumudu transforms. Further, we apply two transforms to solve linear ordinary differential equations with constant coefficients and non constant coefficients

A new fractional derivative involving the normalized sinc function without singular kernel

In this paper, a new fractional derivative involving the normalized sinc function without singular kernel is proposed. The Laplace transform is used to find the analytical solution of the anomalous heat-diffusion problems. The comparative results between classical and fractional-order operators are presented. The results are significant in the analysis of one-dimensional anomalous heat-transfer problems.Comment: Keywords: Fractional derivative, anomalous heat diffusion, integral transform, analytical solutio