Solution of Partial Integro-Differential Equations Involving Mixed Partial Derivatives by Laplace Substitution Method

S.S. Handibag^1, , B. D. Karande² and S. V. Badgire³

¹Department of Mathematics, Mahatma Basweshwar Mahavidyalaya, Latur-413 512, Maharashtra, India

²Departments of Mathematics, Maharashtra Udayagiri Mahavidyalaya, Udgir, Maharashtra India

³Department of Mathematics, Azad Mahavidyalaya, Ausa, Maharashtra, India

Cite this paper:
S.S. Handibag, B. D. Karande and S. V. Badgire. Solution of Partial Integro-Differential Equations Involving Mixed Partial Derivatives by Laplace Substitution Method. American Journal of Applied Mathematics and Statistics. 2018; 6(6):272-280. doi: 10.12691/ajams-6-6-9

Abstract

This paper studies the Laplace substitution method for nonlinear partial integro-differential equations involving mixed partial derivatives and further applications of same method for coupled nonlinear partial integro-differential equations involving mixed partial derivatives.

Keywords:
Laplace substitution method partial integro-differential equations mixed derivatives

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References:

[1]	R. K. Getoor, Markov operators and their associated semi-groups, Pacific J. Math. 9 (1959), 449-472.
[2]	R. M. Blumenthal, R. K. Getoor, The asymptotic distribution of the eigenvalues for a class of Markov operators, Pacific J. Math. 9 (1959), 399-408.
[3]	R. M. Blumenthal, R. K. Getoor, Some theorems on stable processes, Trans. Amer. Math. Soc. 95 (1960), 263-273.
[4]	R. K. Getoor, First passage times for symmetric stable processes in space, Trans. Amer. Math. Soc.101 (1961), 75-90.
[5]	M. Kac, H. Pollard, Partial sums of independent random variables, Canad. J. Math 11 (1950), 375-384.
[6]	R. M. Blumenthal, R. K. Getoor, D. B. Ray, On the distribution of first hits for the symmetric stable processes, Trans. Amer. Math. Soc. 99 (1961), 540-554.
[7]	M. Riesz, Integrales de Riemann-Liouville et potentiels, Acta Sci. Math. Szeged, 1938.
[8]	N. E. Humphries et al., Environmental context explains Levy and Brownian movement patterns of marine predators, Nature, 465 (2010), 1066-1069.
[9]	A. M. Reynolds, C. J. Rhodes, the Levy fight paradigm: Random search patterns and mechanisms, Ecology 90 (2009), 877-887.
[10]	G. M. Viswanathan et al., Levy fight search patterns of wandering albatrosses, Nature 381 (1996), 413-415.
[11]	S. S. Handibag, B.D. Karande, An Application for nonlinear Partial Differential Equations Involving Mixed Partial Derivatives by LSM, AIP Conference Proceeding 1637, 384, 2014.
[12]	S. S. Handibag, B.D. Karande, An Extended Application of Laplace Substitution Method, International Journal of scientific and Innovative Mathematical Research, Volume 3, Special Issue 2015, 568-574, ISSN: 2347-307X, (Print), www.arcjournals.org.
[13]	S. S. Handibag, B. D. Karande, Laplace Substitution Method for nth order Linear and Nonlinear Partial Differential Equations Involving Mixed Partial Derivatives, International Research Journal of Engineering and Technology, Volume 2, Issue 9, 2015, P-ISSN: 2395-0072, e-Issn: 2395-0056.