Nonlinear functional differential equations of arbitrary orders

Nonlinear Analysis, Theory, Methods and Applications

Volumn 33, Issue 2, 1998, Pages 181-186

  El Sayed, Ahmed M A ^a  

^a Alexandria University Faculty Of Science   (Egypt)

Author keywords

Fractional calculus; Functional equations; Measure of noncompactness

Indexed keywords

FUNCTIONS; INITIAL VALUE PROBLEMS; MATHEMATICAL OPERATORS; MATHEMATICAL TRANSFORMATIONS; NONLINEAR EQUATIONS; THEOREM PROVING;

ARBITRARY ORDERS; CARATHEODORY CONDITIONS; LIPSCHITZ CONDITIONS; RIEMANN-LIOUVILLE OPERATORS;

DIFFERENTIAL EQUATIONS;

EID: 0032115069     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(97)00525-7     Document Type: Article

References (14)

1. El-Sayed, A. M. A. and Ibrahim, A. G., Multivalued fractional diffential equations. Apll. Math. Comput., 1995, 68, 15-25.
2. El-Sayed, A. M. A., Fractional order evolution equations. J. of Factional Calculus, 1995, 7, 89-101.
3. El-Sayed, A. M. A., Fractional differential difference equations. J. of Fractional Calculus, 1996, 10.
4. El-Sayed, A. M. A., Fractional order diffusion-wave equation. International J. of Theoretical Physics, 1996, 35(2), 311-322.
5. Gelfand, I. M. and Shilov, G. E. Generalized Functions, Vol. 1. Moscow, 1958.
6. Miller, K. S. and Ross, B., An Introduction to the Fractional Calculus and Fractional Diffential Equations. Wiley-Interscierce, New York, 1993.
7. El-Sayed, A. M. A., Linear differential equations of fractional orders. Appl. Math. Comput., 1993, 55, 1-12.
8. Emmanuele, G., Measure of weak noncompactness and fixed point theorem. Bull. Math. Soc. Sci. Math. R.S. Roum., 1981, 25, 253-258.
9. De Blasi, F. S., On a property of the unit sphere in a Banach space. Bull. Math. Soc. Sci. Math. R.S. Roum. (N.S.), 1977, 21, 259-262.
10. Appell, J. and De Pascale, E., Su alcuni parametri connesi con la misura di noncompacttezza di Hausdofff in spazzi functioni misurabili. Boll. Un. Math. Ital., 1984, 3B(6), 497-515.
11. Apostol, T. M., Mathematical Analysis, 6th edn. Adison-Wesley, 1982.
12. Kolmogorov, A. N. and Fomin, S. V., Introductory Real Analysis. Dover, New York, 1975.
13. Banas, J., On the superposition operator and integrable solutions of some functional equations. Nonlinear Analysis, 1988, 12, 777-784.
14. Banas, J. and Goebel, K., Measures of noncompactness in Banach spaces. Lect. Notes in Math. 60. M. Dekker, New York, 1980.