| Title:
|
Weak solution for fractional order integral equations in reflexive Banach spaces (English) |
| Author:
|
Salem, Hussein A. H. |
| Author:
|
El-Sayed, Ahmed M. A. |
| Language:
|
English |
| Journal:
|
Mathematica Slovaca |
| ISSN:
|
0139-9918 |
| Volume:
|
55 |
| Issue:
|
2 |
| Year:
|
2005 |
| Pages:
|
169-181 |
| . |
| Category:
|
math |
| . |
| MSC:
|
26A33 |
| MSC:
|
34A12 |
| MSC:
|
47G10 |
| idZBL:
|
Zbl 1111.26011 |
| idMR:
|
MR2177706 |
| . |
| Date available:
|
2009-09-25T14:25:01Z |
| Last updated:
|
2012-08-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/130333 |
| . |
| Reference:
|
[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. Zbl 0397.34003, MR 0511571 |
| Reference:
|
[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. Zbl 0599.34008, MR 0794756 |
| Reference:
|
[3] BASSAM M.: Some existence theorems on differential equations of generalized order.J. Reine Angew. Math. 218 (1965), 70-78. Zbl 0156.30804, MR 0179405 |
| Reference:
|
[4] CICHOŃ M.: Weak solutions of ordinary differential equations in Banach spaces.Discuss. Math. Differ. Inch Control Optim. 15 (1995), 5-14. MR 1344523 |
| Reference:
|
[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. MR 1876711 |
| Reference:
|
[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. Zbl 0379.34041, MR 0512280 |
| Reference:
|
[7] DIESTEL J.-UHL J. J., Jr.: Vector Measures.Math. Surveys Monogr. 15, Amer. Math. Soc, Providence, R.I., 1977. Zbl 0369.46039, MR 0453964 |
| Reference:
|
[8] EDGAR G. A.: Geometry and the Pettis-integral.Indiana Univ. Math. J. 26 (1977), 663-677. |
| Reference:
|
[9] EDGAR G. A.: Geometry and the Pettis-integral II.Indiana Univ. Math. J. 28 (1979), 559-579. |
| Reference:
|
[10] EL-SAYED A. M.-EL-SAYED W. G.-MOUSTAFA O. L.: On some fractional functional equations.Pure. Math. Appl. 6 (1995), 321-332. Zbl 0867.49001, MR 1399296 |
| Reference:
|
[11] EL-SAYED A. M. A.: Nonlinear functional differential equations of arbitrary orders.Nonlinear Anal. 33 (1998), 181-186. Zbl 0934.34055, MR 1621105 |
| Reference:
|
[12] EL-SAYED A. M. A.-IBRAHIM A. G.: Set-valued integral equations of arbitrary (fractional) order.Appl. Math. Comput. 118 (2001), 113-121. MR 1805164 |
| Reference:
|
[13] GEITZ R. F.: Pettis integration.Proc Amer. Math. Soc 82 (1981), 81-86. Zbl 0506.28007, MR 0603606 |
| Reference:
|
[14] GEITZ R. F.: Geometry and the Pettis integration.Trans. Amer. Math. Soc. 269 (1982), 535-548. MR 0637707 |
| Reference:
|
[15] HADID S. B. : Local and global existence theorem on differential equation on non integral order.Math. Z. 7 (1995), 101-105. MR 1330572 |
| Reference:
|
[16] HILLE E.-PHILLIPS R. S.: Functional Analysis and Semi-groups.Amer. Math. Soc. Colloq. Publ. 31, Amer. Math. Soc, Providence, R.I., 1957. MR 0089373 |
| Reference:
|
[17] KNIGHT W. J.: Solutions of differential equations in B-spaces.Duke Math. J. 41 (1974), 437-442. Zbl 0288.34063, MR 0344624 |
| Reference:
|
[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. Zbl 0516.34058, MR 0710975 |
| Reference:
|
[19] MILLER K. S.-ROSS B.: An Introduction to the Fractional Calculus and Fractional Differential Equations.John Wiley, New York, 1993. Zbl 0789.26002, MR 1219954 |
| Reference:
|
[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. MR 0502554 |
| Reference:
|
[21] O'REGAN D.: Fixed point theory for weakly sequentially continuous mapping.Math. Comput. Modeling 27 (1998), 1-14. |
| Reference:
|
[22] PETTIS B. J.: On integration in vector spaces.Trans. Amer. Math. Soc. 44 (1938), 277-304. Zbl 0019.41603, MR 1501970 |
| Reference:
|
[23] PHILLIPS R. S.: Integration in a convex linear topological space.Trans. Amer. Math. Soc. 47 (1940), 114-115. Zbl 0022.31902, MR 0002707 |
| Reference:
|
[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. |
| Reference:
|
[25] PODLUBNY I.: Fractional Differential Equation.Acad. Press, San Diego-New York-London, 1999. |
| Reference:
|
[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. MR 1949636 |
| Reference:
|
[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. MR 2133908 |
| Reference:
|
[28] SAMKO S.-KILBAS A.-MARICHEV O.: Fractional Integrals and Derivatives: Theory and Applications.Gordon and Breach Sci. PubL, New York, 1993. Zbl 0818.26003, MR 1347689 |
| Reference:
|
[29] VÄTH M.: Ideal spaces.Lecture Notes in Math. 1664, Springer, Berlin-Heidelberg, 1997. Zbl 0896.46018, MR 1463946 |
| Reference:
|
[30] SZEP A.: Existence theorem for weak solutions of differential equations in Banach spaces.Studia Sci. Math. Hungar. 6 (1971), 197-203. MR 0330688 |
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