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19 results on '"Mohamed Houas"'

1. On a Duffing-type oscillator differential equation on the transition to chaos with fractional q-derivatives

Author

Mohamed Houas, Mohammad Esmael Samei, Shyam Sundar Santra, and Jehad Alzabut

Subjects
Duffing differential equation, Existence and uniqueness, Fractional q-difference equations, Ulam–Hyers stability, Mathematics, QA1-939
Abstract

Abstract In this paper, by applying fractional quantum calculus, we study a nonlinear Duffing-type equation with three sequential fractional q-derivatives. We prove the existence and uniqueness results by using standard fixed-point theorems (Banach and Schaefer fixed-point theorems). We also discuss the Ulam–Hyers and the Ulam–Hyers–Rassias stabilities of the mentioned Duffing problem. Finally, we present an illustrative example and nice application; a Duffing-type oscillator equation with regard to our outcomes.

Published
2024
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2. Analysis of the far-field behavior of waves in magnetogasdynamic

Author

Anoop Kumar, Aziz Khan, Rajan Arora, Thabet Abdeljawad, K. Karthikeyan, and Mohamed Houas

Subjects
asymptotic method, magnetogasdynamics, evolution equation, non-linear waves, homotopy analysis method, Mathematics, QA1-939
Abstract

Herein the research objects, a hyperbolic quasi-linear system of governing equations was solved by an asymptotic method (far-field technique) with explaining a 1-D unsteady planar and cylindrically symmetric flows in magnetogasdynamics. The evolution equation was obtained by generalized Burger's equation. A relatively accurate systematic result of the evolution equation was gotten by us through the analytic homotopy analysis method (HAM). We are allowed by the method to determine the various effects of nonlinearity and geometrical spreading. One of the fundamental problems of conservation laws are represented by the non-linear waves from preliminary data.

Published
2023
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3. Existence and stability results of pantograph equation with three sequential fractional derivatives

Author

Mohamed Houas, Kirti Kaushik, Anoop Kumar, Aziz Khan, and Thabet Abdeljawad

Subjects
fractional derivative, fixed point, existence, fractional pantograph equation, mittag-leffler-ulam stability, Mathematics, QA1-939
Abstract

The subject of this work is the existence and Mittag-Leffler-Ulam (MLU) stability of solutions for fractional pantograph equations with three sequential fractional derivatives. Sufficient conditions for the existence and uniqueness of solutions are constructed by utilizing well-known classical fixed point theorems such as the Banach contraction principle, and Leray-Schauder nonlinear alternative. The generalized singular Gronwall's inequality is used to show the MLU stability results. An illustrated example is provided to support the main findings.

Published
2023
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4. Existence and stability analysis to the sequential coupled hybrid system of fractional differential equations with two different fractional derivatives

Author

Mohamed Houas, Jehad Alzabut, and Mahammad Khuddush

Subjects
Coupled systems, Hybrid differential equations, Boundary value problem, Fractional derivative, Ulam-Hyers stability, Applied mathematics. Quantitative methods, T57-57.97, Mathematics, QA1-939
Abstract

In this paper, we discussed the existence, uniqueness and Ulam-type stability of solutions for sequential coupled hybrid fractional differential equations with two derivatives. The uniqueness of solutions is established by means of Banach's contraction mapping principle, while the existence of solutions is derived from Leray-Schauder's alternative fixed point theorem. Further, the Ulam-type stability of the addressed problem is studied. Finally, an example is provided to check the validity of our obtained results.

Published
2023
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5. Uniqueness and Ulam–Hyers–Rassias stability results for sequential fractional pantograph q-differential equations

Author

Mohamed Houas, Francisco Martínez, Mohammad Esmael Samei, and Mohammed K. A. Kaabar

Subjects
Pantograph equations, Fractional pantograph q-differential equation, Uniqueness, Ulam–Hyers stability, Mathematics, QA1-939
Abstract

Abstract We study sequential fractional pantograph q-differential equations. We establish the uniqueness of solutions via Banach’s contraction mapping principle. Further, we define and study the Ulam–Hyers stability and Ulam–Hyers–Rassias stability of solutions. We also discuss an illustrative example.

Published
2022
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6. Existence of solutions for nonlinear Hadamard differential equations with nonlocal conditions

Author

Mohamed Houas

Subjects
Differential equation, Applied Mathematics, Mathematical analysis, 010103 numerical & computational mathematics, 02 engineering and technology, Fixed point, 01 natural sciences, Nonlinear system, Hadamard transform, 0202 electrical engineering, electronic engineering, information engineering, 020201 artificial intelligence & image processing, Boundary value problem, Uniqueness, 0101 mathematics, Fractional differential, Contraction principle, Analysis, Mathematics
Abstract

This paper investigates the existence of solutions for a boundary value problem of Hadamard fractional differential equations with nonlocal conditions. The existence and uniqueness of solutions is ...

Published
2020

7. Existence and uniqueness results for a coupled system of nonlinear fractional differential equations with two fractional orders

Author

Mohamed Houas and Abdelkader Saadi

Subjects
Work (thermodynamics), Mathematics::Complex Variables, Applied Mathematics, Fixed-point theorem, 010103 numerical & computational mathematics, 02 engineering and technology, 01 natural sciences, Nonlinear fractional differential equations, 0202 electrical engineering, electronic engineering, information engineering, Applied mathematics, 020201 artificial intelligence & image processing, Uniqueness, 0101 mathematics, Analysis, Mathematics
Abstract

In this work, we discuss the existence of solutions for a coupled system of nonlinear fractional differential equations involving two Riemann-Liouville fractional orders. By applying the Leray-Scha...

Published
2020

8. Some estimations on continuous random variables for (k, s) −fractional integral operators

Author

Mohamed Houas

Subjects
010104 statistics & probability, Numerical Analysis, Control and Optimization, Applied Mathematics, 010102 general mathematics, Applied mathematics, 0101 mathematics, 01 natural sciences, Random variable, Analysis, Mathematics
Abstract

In this work, we establish some new (k, s) −fractional integral inequalities of continuous random variables by using the (k, s) −Riemann-Liouville fractional integral operator.

Published
2020

9. Some integral inequalities for (k, s) – Riemann-Liouville fractional operators

Author

Mohamed Houas, Mehmet Zeki Sarikaya, and Zoubir Dahmani

Subjects
Pure mathematics, Applied Mathematics, Opera, 010103 numerical & computational mathematics, 02 engineering and technology, Riemann liouville, 01 natural sciences, (k, s) - fractional integral, 0202 electrical engineering, electronic engineering, information engineering, 020201 artificial intelligence & image processing, Integral inequalities, Riemann-Liouville fractional integral, 0101 mathematics, Analysis, Mathematics
Abstract

WOS: 000456137400008 In this paper, by using a new fractional integral approach of M.Z. Sarikaya et al., we establish new generalized fractional integral inequalities involving (k, s) - Riemann-Liouville integral operators. Some classical and non classical integral inequalities can be deduced as some special cases.

Published
2018

10. New integral inequalities for (r,alpha)-fractional moments of continuous random variables

Author

Mohamed Houas, Zoubir Dahmani, and Mehmet Zeki Sarikaya

Subjects
Fractional dispersion, Fractional moment, Fractional variance, Integral inequalities, Random variable, Riemann-liouville integral, General Mathematics, Alpha (ethology), Applied mathematics, Mathematics
Abstract

In this paper, we establish new integral inequalities for continuous random variables. By introducing new concepts on fractional moments of continuous random variables, we generalize some interesting results of P. Kumar. Other fractional integral results are also presented. © 2018, Publishing House of the Romanian Academy. All rights reserved.

Published
2018

11. Existence of Solutions for Fractional Differential Equations Involving Two Riemann-Liouville Fractional Orders

Author

Mohamed Houas

Subjects
Applied Mathematics, 0202 electrical engineering, electronic engineering, information engineering, 020201 artificial intelligence & image processing, 010103 numerical & computational mathematics, 02 engineering and technology, 0101 mathematics, Riemann liouville, Fractional differential, 01 natural sciences, Analysis, Mathematics, Mathematical physics
Published
2018

12. Some integral inequalities involving Saigo fractional integral operators

Author

Mohamed Houas

Subjects
Algebra, Operator (computer programming), Applied Mathematics, 010102 general mathematics, 010103 numerical & computational mathematics, 0101 mathematics, 01 natural sciences, Analysis, Mathematics
Abstract

In this paper, the Saigo fractional integral operator is used to generate some new integral inequalities. By using the Saigo fractional integral operator, we also generate new classes of integral i...

Published
2018

14. On existence of solutions for fractional differential equations with nonlocal multi-point boundary conditions

Author

Mohamed Houas and Zoubir Dahmani

Subjects
Picard–Lindelöf theorem, Banach fixed-point theorem, General Mathematics, 010102 general mathematics, Mathematical analysis, Fixed-point theorem, 01 natural sciences, Fractional calculus, 010101 applied mathematics, Initial value problem, Uniqueness, Boundary value problem, 0101 mathematics, Fractional differential, Mathematics
Abstract

This paper investigates the existence of solutions for a boundary value problem of nonlinear fractional differential equations with nonlocal boundary conditions. We use Banach fixed point theorem to prove an existence and uniqueness result. Then, by using O’Regan fixed point theorem, we prove an existence result. Finally, illustrative examples of our main results are presented.

Published
2016

15. EXISTENCE AND UNIQUENESS RESULTS FOR A COUPLED SYSTEM OF HADAMARD FRACTIONAL DIFFERENTIAL EQUATIONS WITH MULTI-POINT BOUNDARY CONDITIONS

Author

Mohamed Houas and Khellaf Ould Melha

Subjects
Hadamard transform, Mathematical analysis, Fixed-point theorem, Uniqueness, Boundary value problem, Fractional differential, Contraction (operator theory), Multi point, Mathematics
Abstract

In this paper, we have studied existence and uniqueness of solutions for a coupled system of multi-point boundary value problems for Hadamard fractional differential equations. By applying principle contraction and Shaefer's fixed point theorem new existence results have been obtained.

Published
2020

16. New results for a system of two fractional differential equations involving n Caputo derivatives

Author

Zoubir Dahmani and Mohamed Houas

Subjects
Differential equation, General Mathematics, Mathematical analysis, Fixed-point theorem, Applied mathematics, Uniqueness, Fractional differential, Contraction principle, Mathematics
Abstract

This paper studies a coupled system of two differential equations of arbitrary orders using Caputo approach with n derivatives, n є N *, n ≠ 1. New existence and uniqueness results are established using Banach contraction principle. Other existence results are obtained using Schaefer and Krasnoselskii fixed point theorems. Some illustrative examples are also presented.

Published
2014

17. EXISTENCE AND STABILITY RESULTS FOR FRACTIONAL DIFFERENTIAL EQUATIONS WITH TWO CAPUTO FRACTIONAL DERIVATIVES

Author

Mohamed Bezziou and Mohamed Houas

Subjects
Nonlinear system, Applied mathematics, Contraction mapping, Uniqueness, Stability result, Fractional differential, Fixed point, Stability (probability), Fractional calculus, Mathematics
Abstract

In this paper, we discuss the existence, uniqueness and stability of solutions for a nonlocal boundary value problem of nonlinear fractional differential equations with two Caputo fractional derivatives. By applying the contraction mapping and O’Regan fixed point theorem, the existence results are obtained. We also derive the Ulam-Hyers stability of solutions. Finally, some examples are given to illustrate our results.

Published
2019

18. New Fractional Results for a Boundary Value Problem with Caputo Derivative

Author

Zoubir Dahmani and Mohamed Houas

Subjects
Point boundary, Mathematical analysis, Applied mathematics, Order (group theory), Point (geometry), Derivative, Boundary value problem, Uniqueness, Value (mathematics), Mathematics
Abstract

In this paper, we consider three point boundary value problem for fractional dierential equations of order 1 < < 2. We establish new conditions for the existence and uniqueness of solutions by using Banach xed point theorem. We also generate other existence results using Scheafer and Krasnoselskii xed point theorems.

Published
2013

19. On Some Boundary Value Problems for a Coupled System of Arbitrary Order

Author

Mohamed Amine Abdellaoui, Mohamed Houas, and Zoubir Dahmani

Subjects
Schauder fixed point theorem, Picard–Lindelöf theorem, Banach fixed-point theorem, Applied mathematics, Initial value problem, Fixed-point theorem, Kakutani fixed-point theorem, Brouwer fixed-point theorem, Peano existence theorem, Biomedical engineering, Mathematics
Abstract

This paper is concerned with the existence of solutions for a coupled system of fractional differential equations with integral conditions. New existence and uniqueness results are established using Banach fixed point theorem. Other existence results are obtained using Schaefer fixed point theorem. Some illustrative examples are also presented.

Published
2013

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