Volume 34, Issue 2, November 2021, Pages 354–368
Walo Omana Rebecca1 and Kumwimba Seya Didier2
1 Department of Mathematics and Computer Science, Faculty of Science, University of Kinshasa, Kinshasa XI - B.P 190, RD Congo
2 Department of Mathematics and Computer Science, Faculty of Science, University of Lubumbashi, C.R.F.D.M.I., Lubumbashi - B.P 1825, RD Congo
Original language: English
Copyright © 2021 ISSR Journals. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
This paper deals with abstract version of the Cauchy Problem in fuzzy normed space. We define a Hausdorff measure of non compactness for bounded fuzzy set to prove existence of solutions by using a sequential approximation of the abstract problem. As a byproduct, we obtain a fuzzy version of the Cauchy-Kowaleskya Theorem for the generalized Hukuhara nonlinear partial differential equations.
Author Keywords: Fuzzy normed spaces, generalized Hukuhara derivative, Hausdorff measure of non compacteness.
Walo Omana Rebecca1 and Kumwimba Seya Didier2
1 Department of Mathematics and Computer Science, Faculty of Science, University of Kinshasa, Kinshasa XI - B.P 190, RD Congo
2 Department of Mathematics and Computer Science, Faculty of Science, University of Lubumbashi, C.R.F.D.M.I., Lubumbashi - B.P 1825, RD Congo
Original language: English
Copyright © 2021 ISSR Journals. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
This paper deals with abstract version of the Cauchy Problem in fuzzy normed space. We define a Hausdorff measure of non compactness for bounded fuzzy set to prove existence of solutions by using a sequential approximation of the abstract problem. As a byproduct, we obtain a fuzzy version of the Cauchy-Kowaleskya Theorem for the generalized Hukuhara nonlinear partial differential equations.
Author Keywords: Fuzzy normed spaces, generalized Hukuhara derivative, Hausdorff measure of non compacteness.
How to Cite this Article
Walo Omana Rebecca and Kumwimba Seya Didier, “Cauchy-Kowaleskya problem in fuzzy normed spaces,” International Journal of Innovation and Applied Studies, vol. 34, no. 2, pp. 354–368, November 2021.
