Browsing by Author "Ardjouni Abdelouaheb"

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    Existence and uniqueness of positive solutions for first-order nonlinear Liouville-Caputo fractional differential equations
    (University Of Eloued جامعة الوادي, 2020-02-23) Haoues Moussa; Ardjouni Abdelouaheb
    We study the existence and uniqueness of positive solutions of the rst-order nonlinear Liouville Caputo fractional differential equation ........................................................ ........................................................ where ....... In the process we convert the given fractional differential equation into an equivalent integral equation. Then we construct appropriate mappings and employ the Krasnoselskii xed point theorem and the method of upper and lower solutions to show the existence of a positive solution of this equation. We also use the Banach xed point theorem to show the existence of a unique positive solution.
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    Existence and uniqueness of positive solutions for hybrid nonlinear fractional differential equations
    (University Of Eloued جامعة الوادي, 2020-02-23) Haoues Moussa.; Ardjouni Abdelouaheb
    In this paper, we study the existence, uniqueness, monotonicity and positivity of the solution of hybrid nonlinear fractional differential equations by the method of upper and lower control functions and using Dhage and Banach fixed point theorem. Two examples of the obtained results is given
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    Initial-value problems for nonlinear hybrid implicit Caputo fractional differential equations
    (University Of Eloued جامعة الوادي, 2020-02-23) Lachouri Adel; Ardjouni Abdelouaheb
    We study the existence and uniqueness of solutions of a nonlinear hybrid implicit Caputo fractional differential equation ................................... ................................... .................................. where.................is the Caputo fractional derivative of order ................... In the process we convert the given fractional differential equation into an equivalent integral equation. Then we construct an appropriate mapping and employe the Banach’s fixed point theorem to show the existence and uniqueness of solutions of this equation. We also use the generalization of Gronwall’s inequality to show the estimate of the solution. Keywords: Implicit fractional differential equations, Caputo fractional derivatives, fixed point theorems, existence, uniqueness.