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A Global Existence and Uniqueness Theorem for Ordinary Differential Equations of Generalized Order

Published online by Cambridge University Press:  20 November 2018

Ahmed Z. Al-Abedeen  and
H. L. Arora
Ahmed Z. Al-Abedeen
Affiliation:
Dept. of Mathematics, College of Science, Mosul University, Mosul-Iraq
H. L. Arora
Affiliation:
Dept. of Mathematics, College of Science, Mosul University, Mosul-Iraq
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Abstract

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We extend the Picard's theorem to ordinary differential equation of generalized order α, 0 ≤ α ≤ l, and prove a global existence and uniqueness theorem by using the Banach contraction principle.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 21 , Issue 3 , 01 September 1978 , pp. 267 - 271
Copyright
Copyright © Canadian Mathematical Society 1978

References

1. Al-Abedeen, Ahmed Z., Existence theorem on differential equations of generalized order, Rafidain Journal of Science, Mosul Univ.-IRAQ, Vol. 1 (1976, pp. 95-104).Google Scholar
2. Barrett, J. H., Differential equations of non-integer order, Can. J. Math. 6 (1954, pp. 529-541).Google Scholar
3. Al-Bassam, M. A., Some existence theorems on differential equations of generalized order, (Presented to the Mathematical Association of America-Texas Section), April 10, 1964.Google Scholar
4. Chu, S. C. and Diaz, J. B., A fixed point theorem for ‘in large’ application of the contraction principle, A. D. Ac. di Torino, Vol. 99 (1964-65, pp. 351-363).Google Scholar
5. Derrick, W. and Janos, L., A global existence and uniqueness theorem for ordinary differential equations, Can. Math. Bull. Vol. 19(1) (1976, pp. 105-107).Google Scholar
6. Royden, H. L., Real Analysis, The Macmillan Company, New York, 1968.Google Scholar