A New Sequential Proportional Fractional Derivative of Hybrid Differential Equations with Nonlocal Hybrid Condition

Open Access

Original research article

Author(s):

Hamid Beddani^a, Moustafa Beddani^b, Saada Hamouda^c

^a Laboratory of Complex Systems of the Higher School of Electrical and Energy Engineering, Oran, Algeria.
^b Department of Mathematics, E.N.S of Mostaganem, Mostaganem, Algeria.
^c Laboratory of Pure and Applied Mathematics, Abdelhamid Ibn Badis University, Mostaganem, Algeria.

Advances in the Theory of Nonlinear Analysis and its Applications 8(1), 148-161.

Received: May 26, 2022

Accepted: December 20, 2022

Published: January 4, 2023

Abstract

In this paper, we study the existence of solutions for a new problem of hybrid differential equations with nonlocal integro multi-point boundary conditions by using the proportional fractional derivative. The presented results are obtained by using hybrid fixed point theorems for three Dhage operators. The application of theoretical conclusions is demonstrated through an example.

Keywords: Hybrid fixed point theorem, proportional fractional derivative, existence of solution.

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APA Style

Beddanı, H., Moustafa, B., & Hamouda, S. (2023). A new sequential proportional fractional derivative of hybrid differential equations with nonlocal hybrid condition. Advances in the Theory of Nonlinear Analysis and its Application, 7(1), 148-161.