Gaafar, F. (2014). Continuous and integrable solutions of a nonlinear Cauchy problem of fractional order with nonlocal conditions. test, 22(3), 341-347.
F.M. Gaafar. "Continuous and integrable solutions of a nonlinear Cauchy problem of fractional order with nonlocal conditions". test, 22, 3, 2014, 341-347.
Gaafar, F. (2014). 'Continuous and integrable solutions of a nonlinear Cauchy problem of fractional order with nonlocal conditions', test, 22(3), pp. 341-347.
Gaafar, F. Continuous and integrable solutions of a nonlinear Cauchy problem of fractional order with nonlocal conditions. test, 2014; 22(3): 341-347.

Continuous and integrable solutions of a nonlinear Cauchy problem of fractional order with nonlocal conditions

Journal of the Egyptian Mathematical Society
Volume 22, Issue 3, October 2014, Pages 341-347    PDF (502.83 K)
Document Type: Original Article
Author
F.M. Gaafar
Faculty of Science, Damanhour University, Damanhour, Egypt
Abstract
In this article, we discuss the existence of at least one solution as well as uniqueness for a
nonlinear fractional differential equation with weighted initial data and nonlocal conditions. The
existence of at least one L1 and continuous solution will be proved under the Carathe`odory conditions via a classical fixed point theorem of Schauder. An example is also given to illustrate the efficiency of the main theorems.
Keywords
Nonlinear fractional problem; Riemann–Liouville fractional derivative; Weighted Cauchy problem; Nonlocal condition; Schauder fixed point theorem
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