Paper's Title:

An Efficient Modification of Differential Transform Method for Solving Integral and Integro-differential Equations

Author(s):

S. Al-Ahmad, Ibrahim Mohammed Sulaiman^*, and M. Mamat

Faculty of Informatics and Computing,
Universiti Sultan Zainal Abidin,
Terengganu, Besut Campus, 22200,
Malaysia.
E-mail: Alahmad.shadi@yahoo.com, ^*sulaimanib@unisza.edu.my, must@unisza.edu.my
 

Abstract:

In this paper, classes of integral and integro-differential equations are solved using a modified differential transform method. This proposed technique is based on differential transform method (DTM), Laplace transform (LT) procedure and Pad\'{e} approximants (PA). The proposed method which gives a good approximation for the true solution in a large region is referred to modified differential transform method (MDTM). An algorithm was developed to illustrate the flow of the proposed method. Some numerical problems are presented to check the applicability of the proposed scheme and the obtained results from the computations are compared with other existing methods to illustrates its efficiency. Numerical results have shown that the proposed MDTM method is promising compared to other existing methods for solving integral and integro-differential equations.

Paper's Title:

SEVERAL q-INTEGRAL INEQUALITIES

Author(s):

W. T. Sulaiman

Department of Computer Engineering,
College of Engineering,
University of Mosul,
Iraq.

 waadsulaiman@hotmail.com
 

Abstract:

In the present paper several q-integral inequalities are presented, some of them are new and others are generalizations of known results.

Paper's Title:

Turan Type Inequalities for Some Special Functions

Author(s):

W. T. Sulaiman

Department of Computer Engineering,
College of Engineering,
University of Mosul,
Iraq

waadsulaiman@hotmail.com

 

Abstract:

In this paper new results concerning the q-polygamma and q-zeta functions are presented. Other generealizations of some known results are also obtained.

Paper's Title:

General Extension of Hardy-Hilbert's Inequality (I)

Author(s):

W. T. Sulaiman

College of Computer Science and Mathematics, University of Mosul,
Iraq.
waadsulaiman@hotmail.com

Abstract:

A generalization for Hardy-Hilbert's inequality that extends the recent results of Yang and Debnath [6], is given.

Paper's Title:

Ostrowski Type Inequalities for Lebesgue Integral: a Survey of Recent Results

Author(s):

Sever S. Dragomir^1,2

¹Mathematics, School of Engineering & Science
Victoria University, PO Box 14428
Melbourne City, MC 8001,
Australia
E-mail: sever.dragomir@vu.edu.au

 
²DST-NRF Centre of Excellence in the Mathematical and Statistical Sciences,
School of Computer Science & Applied Mathematics,
University of the Witwatersrand,
Private Bag 3, Johannesburg 2050,
South Africa
URL: http://rgmia.org/dragomir 

Abstract:

The main aim of this survey is to present recent results concerning Ostrowski type inequalities for the Lebesgue integral of various classes of complex and real-valued functions. The survey is intended for use by both researchers in various fields of Classical and Modern Analysis and Mathematical Inequalities and their Applications, domains which have grown exponentially in the last decade, as well as by postgraduate students and scientists applying inequalities in their specific areas.

Paper's Title:

Hermite-Hadamard Type Inequalities for MN-Convex Functions

Author(s):

Sever S. Dragomir^1,2

¹Mathematics, College of Engineering & Science
Victoria University, PO Box 14428
Melbourne City, MC 8001,
Australia
E-mail: sever.dragomir@vu.edu.au

 
²DST-NRF Centre of Excellence in the Mathematical and Statistical Sciences,
School of Computer Science & Applied Mathematics,
University of the Witwatersrand,
Private Bag 3, Johannesburg 2050,
South Africa
URL: https://rgmia.org/dragomir 

Abstract:

The present work endeavours to briefly present some of the fundamental results connected to the Hermite-Hadamard inequality for special classes of convex functions such as AG, AH, GA, GG, GH, HA, HG and HH -convex functions in which the author have been involved during the last five years. For simplicity, we call these classes of functions such as MN-convex functions, where M and N stand for any of the Arithmetic (A), Geometric (G) or Harmonic (H) weighted means of positive real numbers. The survey is intended for use by both researchers in various fields of Approximation Theory and Mathematical Inequalities, domains which have grown exponentially in the last decade, as well as by postgraduate students and scientists applying inequalities in their specific areas.

Paper's Title:

Generalizations of two theorems on absolute summability methods

Author(s):

H.S. Özarslan and H.N. Öğdük

Abstract:

In this paper two theorems on summability methods, which generalize two theorems of Bor on summability methods, have been proved.

Paper's Title:

Some Generalizations of Steffensen's Inequality

Author(s):

W. T. Sulaiman

College of Computer Science and Mathematics
University of Mosul , Iraq

Abstract:

Some generalization of Steffensen's inequalities are given.

Paper's Title:

Numerical Solution of Certain Types of Fredholm-Volterra Integro-Fractional Differential Equations via Bernstein Polynomials

Author(s):

Alias B. Khalaf¹, Azhaar H. Sallo² and Shazad S. Ahmed³

¹Department of Mathematics, College of Science,
University of Duhok,
Kurdistan Region,
Iraq.
E-mail:  aliasbkhalaf@uod.ac

²Department of Mathematics, College of Science,
University of Duhok,
Kurdistan Region,
Iraq.
E-mail:  azhaarsallo@uod.ac

³Department of Mathematics, College of Science,
University of Sulaimani,
Kurdistan Region,
Iraq.
E-mail: shazad.ahmed@univsul.edu

Abstract:

In this article we obtain a numerical solution for a certain fractional order integro-differential equations of Fredholm-Volterra type, where the fractional derivative is defined in Caputo sense. The properties of Bernstein polynomials are applied in order to convert the fractional order integro-differential equations to the solution of algebraic equations. Some numerical examples are investigated to illustrate the method. Moreover, the results obtained by this method are compared with the exact solution and with the results of some existing methods as well.

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