Solutions of Integral Nonclassical Ordinary Differential Equations Via Contractor Maps

S. A. Bishop, K. S. Eke, H. Akewe, G. Okeke

Abstract


Existence of a unique and bounded stochastic solution of integral nonclassical ordinary differential equation is studied using the method of integral contractor operators.


Keywords


Unique solution; Integral NODE; Random Contractors; Stochastic processes

Full Text:

PDF

References


M. Altman, Contractor directions, directional contractors and directional contractions for solving equations, Pacific Journal of Mathematics 62(1) (1976), 1 – 18.

E.O. Ayoola, On convergence of one-step schemes for weak solutions of quantum stochastic differential equations, Acta Applicandae Mathematicae 67 (2001), 19 – 58.

K. Balachandran and J.H. Kim, Existence of solutions of nonlinear stochastic volterra fredholm integral equations of mixed type, International Journal of Mathematics and Mathematical Sciences 2010 (2010), Article ID 603819, 16 pages.

S.A. Bishop, On continuous selection sets of non-Lipschitzian quantum stochastic evolution inclusions, International Journal of Stochastic Analysis 2015 (2015), Article ID 834194, 5 pages.

S.A. Bishop and E.O. Ayoola, On topological properties of solution sets of non Lipschitzian quantum stochastic differential inclusions, Journal of Analysis and Mathematical Physics (Sept, 2015), http://link.springer.com/article/10.1007/s13324-015-0109-1.

S.A. Bishop, M.C. Agarana, O.O. Agboola, G.J. Oghonyon and T.A. Anake, Existence, uniqueness and stability of mild solution of Lipschitzian quantum stochastic differential equations, Advances in Differential Equations and Control Processes 14(2) (2014), 99 – 116.

H.-H. Kuo, On integral contractors, Journal of Integral Equations 1(1) (1979), 35 – 46.

A.C.H. Lee and W.J. Padgett, On a class of stochastic integral equations of mixed type, Inform. Contr. 34 (1977), 339 – 347.

M. Nouri-Moghadam and T. Yoshimura, Applications of Altman, Contractor techniques to nonlinear integral equations for Green’s functions of augmented quantum field’s theory, Jour. of Math. Physics 20(1) (1979), DOI: 10.1063/1.523944.

G.M. Mophou and G.M. N’Gurkata, On integral solutions of some nonlocal fractional differential equations with nondense domain, Nonlinear Analysis 71 (2009), 4668 – 4675.

W.J. Padgett and A.N.V. Rao, Solutions of a Stochastic integral equation using integral contractors, Information and Control 41 (1979), 56 – 66.

K.B. Reddy and P.V. Subrahmanyam, Altman’s contractors and fixed points of multivalued mappings, Pacific Journal of Mathematics 99(1) (1982), 127 – 136.

V. Sree Hari Rao, On random solutions of volterra-fredholm integral equations, Pacific Journal of Mathematics 108(2) (1983), 397 – 405.

R. Subramaniam, K. Balachandran and J.K. Kim, Existence of random solutions of a general class of stochastic functional integral equations, Stochastic Analysis and Applications 21(5) (2003), 1189 – 1205.

D. Szynal and S. Wedrychowicz, On solutions of some nonlinear stochastic integral equations, Yokohama Mathematical Journal 41(1) (1993), 31 – 37.

P.C. Tsokos and W.J. Padgett, Random Integral Equations With Applications to Life Sciences and Engineering, Academic Press, New York — London (1974).

D. Xie-Ping, Random directional contractors and their applications, Applied Mathematics and Mechanics 7(12) (1986), 1175 – 1188.


Refbacks

  • There are currently no refbacks.


eISSN 0975-8607; pISSN 0976-5905