Abstract

In this thesis, we are interested in the discussion of the qualitative analysis of some kinds of nonlinear fractional differential equations with or without delay. After a short introduction and some preliminaries on fractional integrals, fractional derivatives, fixed point theorems and fractional delay differential equations, etc. We use the fixed point technique to prove the existence and uniqueness of solutions for a class of nonlinear fractional differential equations with or without delay. We also use the method of successive approximations to show the Ulam stability. Finally, we study the existence, uniqueness and monotonicity of positive solutions for a class of hybrid fractional integro-differential equations. All results obtained in this thesis are illustrated by some examples.
Keywords: Fixed point theory, successive approximations, existence, uniqueness, stability, positivity, fractional differential equations, delay.
Mathematics Subject Classification: 34A08, 34B15, 34B18, 34K20, 45N05, 47H10.

Information

Item Type:	Thesis
Divisions:	» Laboratory of Computer Science and Mathematics
ePrint ID:	2668
Date Deposited:	2021-07-18
Further Information:	Google Scholar
URI:	https://www.univ-soukahras.dz/en/publication/article/2668

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