ON CERTAIN CLASSES OF SEQUENTIAL NONLINEAR BOUNDARY PROBLEMS OF ARBITRARY ORDER

Abstract

In this thesis, we are concerned with the study of certain classes of nonlinear sequential differential equations of arbitrary order. We first propose to explore the domain of integral inequalities according to the two approaches: Hadamard, Riemann-Liouville. Then, using the theory of nonlinear operators, the theory of fixed points as well as the derivative approaches of Caputo, Riemann-liouville and Hadamard, we establish new results on the existence and uniqueness of the solutions for the considered sequential classes. Other existence results are also established. Some other sufficient conditions for the existence of results for our considered classes also imposed. Each chapter is illustrated by some examples that show the applicability of the obtianed results. .