Journal of Ultra Scientist of Physical Sciences - A
Voulume: 30
Issue: 9
Article No. 1
Reduction of Certain Type of Parabolic Partial Differential Equations to Heat Equation
Lecturer in Mathematics, Government Polytechnic, Himmatnagar - 383001 (India)
Former Head of The Department of Mathematics, School of Sciences, Gujarat University Ahmedabad - 380009 (India)
Abstract :

As we all know that the solution of Heat Equation is found more easily than other Partial Differential Equations of Parabolic Type. So, if we enable us to convert Parabolic Partial Differential Equations to Heat Equation, then it becomes easier to find solutions. In this paper we are considering a method introduced by Harper and with the help of a method for reduction of some types of Partial Differential Equations to their Canonical Form it is shown that all the equations of this type are reduced to Heat Equation by following some definite steps. To illustrate the method, we have taken some PDEs of this type and converted them to their Canonical Form and then to Heat Equation.

Keyword : Parabolic Partial Differential Equation, Heat Equation, Solution of First Order Linear PDE, AMS Subject Classification(2010): 35K05; 35K10; 35F05; 35A25
Paper Download Count : 570
View Count : 716
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Article No. 2
Fixed Point Theorems and its Applications in Partial and Generalized Partial Cone Metric Spaces
H.No. 100, Gomti colony, Nehru Nagar, Bhopal (India)
Professor, Department of Mathematics, Safia Science College, Bhopal (India)
Professor and HOD, Department of Mathematics, Chandra Shekhar Azad Govt. P.G. College, Sehore (India)
Abstract :

The main purpose of this paper is to prove some fixed point theorems and its applications in partial and generalized partial cone metric spaces. Our results are satisfying various contractive conditions on cone spaces. We also prove the uniqueness of such fixed points theorems

Keyword : Fixed Point Theorems, Partial Cone Metric Spaces
Paper Download Count : 497
View Count : 730
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Article No. 3
Fixed Point Theorems for Set Valued Contraction Integral Type in Complete Metric Space
Department of Mathematics, Govt. Girls College, Sehore (India)
Department of Mathematics, CSA Govt. P.G. College, Sehore, M.P. (India)
Abstract :

In this paper, we shall establish some stability results for Picard and Mann iteration processes in metric space and normed linear space by employing a set-valued contractive condition of integral type.

Keyword : Contraction Integral Type, Fixed Point Theorems
Paper Download Count : 469
View Count : 782
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