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.
Gaafar, F. (2014). Continuous and integrable solutions of a nonlinear Cauchy problem of fractional order with nonlocal conditions. Journal of the Egyptian Mathematical Society, 22(3), 341-347.
MLA
F.M. Gaafar. "Continuous and integrable solutions of a nonlinear Cauchy problem of fractional order with nonlocal conditions", Journal of the Egyptian Mathematical Society, 22, 3, 2014, 341-347.
HARVARD
Gaafar, F. (2014). 'Continuous and integrable solutions of a nonlinear Cauchy problem of fractional order with nonlocal conditions', Journal of the Egyptian Mathematical Society, 22(3), pp. 341-347.
VANCOUVER
Gaafar, F. Continuous and integrable solutions of a nonlinear Cauchy problem of fractional order with nonlocal conditions. Journal of the Egyptian Mathematical Society, 2014; 22(3): 341-347.
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