American Journal of Mathematical Analysis

ISSN (Print): 2333-8490

ISSN (Online): 2333-8431

Website: http://www.sciepub.com/journal/AJMA

Current Issue» Volume 3, Number 2 (2015)

Article

Similar Constructing Method for Solving the Boundary Value Problem of the Compound Kummer Equation

1College of Science, Xihua University, Chengdu, China

2Beijing Dongrunke Petroleum Technology Co., Ltd., Beijing, China


American Journal of Mathematical Analysis. 2015, 3(2), 39-43
DOI: 10.12691/ajma-3-2-3
Copyright © 2015 Science and Education Publishing

Cite this paper:
Duo Zhang, Shunchu Li, Dongdong Gui. Similar Constructing Method for Solving the Boundary Value Problem of the Compound Kummer Equation. American Journal of Mathematical Analysis. 2015; 3(2):39-43. doi: 10.12691/ajma-3-2-3.

Correspondence to: Shunchu  Li, College of Science, Xihua University, Chengdu, China. Email: lishunchu@163.com

Abstract

This article is devoted to analyze the compound Kummer equation. Through the structure of left region and right region similarity kernel function, have similar structure of solution for this boundary value problems. The left field solution of this kind of boundary value problems can be obtained by combing the coefficients of boundary value problems on the left and the left area similar kernel function. The right field solution of this kind of boundary value problems can be expressed by assembling the left, the right area similar kernel function, the left lead solution functions and the coefficients of the convergence conditions. Thus put forward the simple method which was named similar constructive method to solve the boundary value problems of the compound Kummer equation. The put forward of this method provides the convenience for solving this kind of differential equation boundary value problems.

Keywords

References

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Article

Analytic Solution of Linear Fractional Differential Equation with Jumarie Derivative in Term of Mittag-Leffler Function

1Department of Mathematics, Nabadwip Vidyasagar College, Nabadwip, Nadia, West Bengal, India

2Department of Applied Mathematics, University of Calcutta, Kolkata, West Bengal, India

3Reactor Control System Design Section Bhabha Atomic Research Centre, Mumbai, India

4Department of Physics, Jadavpur University Kolkata, West Bengal, India


American Journal of Mathematical Analysis. 2015, 3(2), 32-38
DOI: 10.12691/ajma-3-2-2
Copyright © 2015 Science and Education Publishing

Cite this paper:
Uttam Ghosh, Srijan Sengupta, Susmita Sarkar, Shantanu Das. Analytic Solution of Linear Fractional Differential Equation with Jumarie Derivative in Term of Mittag-Leffler Function. American Journal of Mathematical Analysis. 2015; 3(2):32-38. doi: 10.12691/ajma-3-2-2.

Correspondence to: Uttam  Ghosh, Department of Mathematics, Nabadwip Vidyasagar College, Nabadwip, Nadia, West Bengal, India. Email: uttam_math@yahoo.co.in

Abstract

There is no unified method to solve the fractional differential equation. The type of derivative here used in this paper is of Jumarie formulation, for the several differential equations studied. Here we develop an algorithm to solve the linear fractional differential equation composed via Jumarie fractional derivative in terms of Mittag-Leffler function; and show its conjugation with ordinary calculus. In these fractional differential equations the one parameter Mittag-Leffler function plays the role similar as exponential function used in ordinary differential equations.

Keywords

References

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Article

Similar Construction Method of the Boundary Value Problem of Composite Spherical Bessel Equations

1Institute of Applied Mathematics, Xihua University, Chengdu, China

2Beijing Dong run ke Petroleum Technology Co,Ltd, Beijing, China


American Journal of Mathematical Analysis. 2015, 3(2), 26-31
DOI: 10.12691/ajma-3-2-1
Copyright © 2015 Science and Education Publishing

Cite this paper:
Qiang Wang, Shunchu Li, Ming Hu, Dongdong Gui. Similar Construction Method of the Boundary Value Problem of Composite Spherical Bessel Equations. American Journal of Mathematical Analysis. 2015; 3(2):26-31. doi: 10.12691/ajma-3-2-1.

Correspondence to: Qiang  Wang, Institute of Applied Mathematics, Xihua University, Chengdu, China. Email: wangqian1205@foxmail.com

Abstract

Aimed at the boundary value problem of composite spherical Bessel equations. Through introducing similar kernel function in the left (right) region, the similar structure of solution was obtained. By analyzing the structure of solution, the solution in the left region was assembled by coefficient of left boundary value condition and similar kernel function in the left region, the solution in the right region was assembled by similar kernel function in the left (right) region; coefficient of left boundary value condition; left guide functions and coefficient of joint conditions. Thus a simple method of solving the boundary value problem of composite spherical Bessel equations is put forward, namely similar construction method; This method provides a way for solving boundary value problem of composite differential equations.

Keywords

References

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8]  Pengshe Zheng, Shunchu Li, Weibing Zhu. The similar structure of pressure distribution in the double porosity composite reservoir (in Chinese). Drilling & Production Technology, 2008, 31 (4): 80-81.
 
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13]  Quanyong Li, Shunchu Li, Ke Li, etc. Study of the seepage model in dual-porosity composite media reservoir based on similar structure of solution (in Chinese). Drilling & Production Technology, 2012, 35 (2): 54-56.
 
14]  Xitao Bao, Shunchu Li, ZhiJian Liao. Similar constructive method of solution for the boundary value problem of Euler Hyper-geometric differential equation (in Chinese). Journal of Southwest University of Science and Technology, 2012, 27 (4): 101-105.
 
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