On solution for fractional differential equations using upper and lower solutions method

Abstract

We are interested in this memory in nonlinear differential equations,this type of equations describes many phenomena.The objective of this memory is to study the approximate solution for solving a class of nonlinear differential equation Caputo-Hadamard fractionalderivativeofvariableorderusingupperandlowermethoditisalsodiscused the upper and lower methode for their solution,that are applied to FDE and systems of FDE.Upper and lower technique is suggested and studied in detail.However,the proprities of Caputo and Hadamard derivatives are also given with complecte details to approximate the solution finite or infinite functions(trigonometric,exponential,logarithmic,and others)are called infinite.The relation between Caputoand Hadamard offractional derivative took a big role for simplifying that represents the containts of Integrable varriable problems.The approximate solution are defined on interval and are compared wich the exact solution of order one wich is an important condition to support the working method.Finally ,illutrative examples are included to confirm the eficiency and accuracy of the proposeed method