Weak solution for fractional order integral equations in reflexive Banach spaces

 Access to full text

 Full (PDF)

1. AL-ABEDEEN A. Z.-ARORA H. L., A global existence and uniqueness theorem for ordinary differential equations of generalized order, Canad. Math. Bull. 21 (1978), 267-271. (1978) Zbl0397.34003MR0511571
2. ARINO O.-GAUTIER S.-PENOT T. P., A fixed point theorem for sequentially continuous mappings with application to ordinary differential equations, Funkcial. Ekvac 27 (1984), 273-279. (1984) Zbl0599.34008MR0794756
3. BASSAM M., Some existence theorems on differential equations of generalized order, J. Reine Angew. Math. 218 (1965), 70-78. (1965) Zbl0156.30804MR0179405
4. CICHOŃ M., Weak solutions of ordinary differential equations in Banach spaces, Discuss. Math. Differ. Inch Control Optim. 15 (1995), 5-14. (1995) MR1344523
5. CICHOŃ M.-EL-SAYED A. M.-SALEM H. A. H., Existence theorem for nonlinear functional integral equations of fractional orders, Comment. Math. Prace Mat. 41 (2001), 59-67. MR1876711
6. CRAMER E.-LAKSHMIKANTHAM V.-MITCHELL A. R., On the existence of weak solutions of differential equations in nonreflexive Banach spaces, Nonlinear Anal. 2 (1978), 259-262. (1978) Zbl0379.34041MR0512280
7. DIESTEL J.-UHL J. J., Jr., Vector Measures, Math. Surveys Monogr. 15, Amer. Math. Soc, Providence, R.I., 1977. (1977) Zbl0369.46039MR0453964
8. EDGAR G. A., Geometry and the Pettis-integral, Indiana Univ. Math. J. 26 (1977), 663-677. (1977) 
9. EDGAR G. A., Geometry and the Pettis-integral II, Indiana Univ. Math. J. 28 (1979), 559-579. (1979) 
10. EL-SAYED A. M.-EL-SAYED W. G.-MOUSTAFA O. L., On some fractional functional equations, Pure. Math. Appl. 6 (1995), 321-332. (1995) Zbl0867.49001MR1399296
11. EL-SAYED A. M. A., Nonlinear functional differential equations of arbitrary orders, Nonlinear Anal. 33 (1998), 181-186. (1998) Zbl0934.34055MR1621105
12. EL-SAYED A. M. A.-IBRAHIM A. G., Set-valued integral equations of arbitrary (fractional) order, Appl. Math. Comput. 118 (2001), 113-121. MR1805164
13. GEITZ R. F., Pettis integration, Proc Amer. Math. Soc 82 (1981), 81-86. (1981) Zbl0506.28007MR0603606
14. GEITZ R. F., Geometry and the Pettis integration, Trans. Amer. Math. Soc. 269 (1982), 535-548. (1982) MR0637707
15. HADID S. B., Local and global existence theorem on differential equation on non integral order, Math. Z. 7 (1995), 101-105. (1995) MR1330572
16. HILLE E.-PHILLIPS R. S., Functional Analysis and Semi-groups, Amer. Math. Soc. Colloq. Publ. 31, Amer. Math. Soc, Providence, R.I., 1957. (1957) MR0089373
17. KNIGHT W. J., Solutions of differential equations in B-spaces, Duke Math. J. 41 (1974), 437-442. (1974) Zbl0288.34063MR0344624
18. KUBIACZYK I.-SZUFLA S., Kneser's theorem for weak solutions of ordinary differential equations in Banach spaces, Publ. Inst. Math. (Beograd) (N.S.) 32(46) (1982), 99-103. (1982) Zbl0516.34058MR0710975
19. MILLER K. S.-ROSS B., An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley, New York, 1993. (1993) Zbl0789.26002MR1219954
20. MITCHELL A. R.-SMITH, CH., An existence theorem for weak solutions of differential equations in Banach spaces, In: Nonlinear Equations in Abstract Spaces. Proc. Int. Symp., Arlington 1977, 1978, pp. 387-403. (1977) MR0502554
21. O'REGAN D., Fixed point theory for weakly sequentially continuous mapping, Math. Comput. Modeling 27 (1998), 1-14. (1998) 
22. PETTIS B. J., On integration in vector spaces, Trans. Amer. Math. Soc. 44 (1938), 277-304. (1938) Zbl0019.41603MR1501970
23. PHILLIPS R. S., Integration in a convex linear topological space, Trans. Amer. Math. Soc. 47 (1940), 114-115. (1940) Zbl0022.31902MR0002707
24. PODLUBNY I.-EL-SAYED A. M. A., On two definitions of fractional calculus, In: Preprint UEF-03-96, Slovak Academy of Sciences, Institute of Experimental Phys., 1996. (1996) 
25. PODLUBNY I., Fractional Differential Equation, Acad. Press, San Diego-New York-London, 1999. (1999) 
26. SALEM H. A. H.-EL-SAYED A. M. A.-MOUSTAFA O. L., Continuous solutions of some nonlinear fractional order integral equations, Comment. Math. Prace Mat. 42 (2002), 209-220. MR1949636
27. SALEM H. A. H.-VÄTH M., An abstract Gronwall lemma and application to global existence results for functional differential and integral equations of fractional order, J. Integral Equations Appl. 16 (2004), 411-439. MR2133908
28. SAMKO S.-KILBAS A.-MARICHEV O., Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach Sci. PubL, New York, 1993. (1993) Zbl0818.26003MR1347689
29. VÄTH M., Ideal spaces, Lecture Notes in Math. 1664, Springer, Berlin-Heidelberg, 1997. (1997) Zbl0896.46018MR1463946
30. SZEP A., Existence theorem for weak solutions of differential equations in Banach spaces, Studia Sci. Math. Hungar. 6 (1971), 197-203. (1971) MR0330688