Search results for: Saïd Abbas

Items from 1 to 20 out of 28 results

article

On implicit fractional q‐difference equations: Analysis and stability

Nadjet Laledj, Abdelkrim Salim, Jamal Eddine Lazreg, Saïd Abbas, more

Mathematical Methods in the Applied Sciences > 45 > 17 > 10775 - 10797

This paper deals with some existence and Ulam stability results for some classes of implicit fractional

q

‐difference equations with and without random effects in Banach spaces and Banach algebras. Our results are provided by applying the fixed point theory (Itoh's random fixed point theorem, the nonlinear alternative of Schaefer's type proved by Dhage, and an other Dhage's random fixed point...

article

The effects of curcumin as dietary supplement for patients with polycystic ovary syndrome: An updated systematic review and meta‐analysis of randomized clinical trials

Basel Abdelazeem, Kirellos Said Abbas, Joseph Shehata, Nischit Baral, more

Phytotherapy Research > 36 > 1 > 22 - 32

This review aims to evaluate if there are clinical benefits of curcumin (CUR) in patients with polycystic ovary syndrome (PCOS). Electronic databases (PubMed, EMBASE, Scopus, Web of Science, Cochrane Central, and Google Scholar) were systematically searched to identify only randomized clinical trials (RCTs) that assessed CUR in patients with PCOS from inception to May 5, 2021. Five RCTs were included...

article

Existence and Ulam stability for implicit fractional q-difference equations

Saïd Abbas, Mouffak Benchohra, Nadjet Laledj, Yong Zhou

Advances in Difference Equations > 2019 > 2019 > 1 > 1-12

This paper deals with some existence, uniqueness and Ulam–Hyers–Rassias stability results for a class of implicit fractional q-difference equations. Some applications are made of some fixed point theorems in Banach spaces for the existence and uniqueness of solutions, next we prove that our problem is generalized Ulam–Hyers–Rassias stable. Two illustrative examples are given in the last section.

article

Caputo–Hadamard fractional differential Cauchy problem in Fréchet spaces

Saïd Abbas, Mouffak Benchohra, Farida Berhoun, Johnny Henderson

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales.... > 2019 > 113 > 3 > 2335-2344

This article deals with some existence results of solutions for a class of differential equations involving the Caputo–Hadamard fractional derivative in Fréchet spaces. These results are based on a generalization of the classical Darbo fixed point theorem for Fréchet spaces associated with the concept of measure of noncompactness. We illustrate our results by an example.

article

Coupled Hilfer fractional differential systems with random effects

Saïd Abbas, Mouffak Benchohra, Yong Zhou

Advances in Difference Equations > 2018 > 2018 > 1 > 1-12

This paper deals with some existence results for two classes of coupled systems of Hilfer and Hilfer–Hadamard random fractional differential equations. The main tool used to carry out our results is Itoh’s random fixed point theorem.

article

Implicit coupled Hilfer–Hadamard fractional differential systems under weak topologies

Saïd Abbas, Mouffak Benchohra, Naima Hamidi, Yong Zhou

Advances in Difference Equations > 2018 > 2018 > 1 > 1-17

In this article, we present some existence of weak solutions for a coupled system of implicit fractional differential equations of Hilfer–Hadamard type. Our approach is based on Mönch’s fixed point theorem associated with the technique of measure of weak noncompactness.

article

A survey on Hadamard and Hilfer fractional differential equations: Analysis and stability

Saïd Abbas, Mouffak Benchohra, Jamal-Eddine Lazreg, Yong Zhou

Chaos, Solitons & Fractals > 2017 > 102 > C > 47-71

In the present survey paper, we prove some results concerning the existence of solutions and weak solutions for some classes of Hadamard and Hilfer fractional differential equations. Some attractivity and Ulam stability results are presented. Our results are provided by applying the fixed point theory, and the technique of strong and weak measures of noncompactness.

article

Stability results for partial fractional differential equations with noninstantaneous impulses

Saïd Abbas, Mouffak Benchohra, Ahmed Alsaedi, Yong Zhou

Advances in Difference Equations > 2017 > 2017 > 1 > 1-22

In this article, we investigate some uniqueness and Ulam’s type stability concepts for the Darboux problem of partial functional differential equations with noninstantaneous impulses and delay in Banach spaces. The main techniques rely on fractional calculus, integral equations and inequalities. Two examples are also provided to illustrate our results.

article

Existence and attractivity for the Darboux problem of fractional order neutral differential equations

Saïd Abbas, Mouffak Benchohra, Johnny Henderson, Boualem Attou Slimani

Journal of Applied Mathematics and Computing > 2016 > 52 > 1-2 > 73-85

In this paper, we prove an existence result and we initiate the question of attractivity of solutions for initial value problems (IVP for short), for fractional order neutral differential equations with finite delay. The proof of the main result is based on Krasnosel’skii’s fixed point theorem.

article

Ulam stabilities for partial Hadamard fractional integral equations

Saïd Abbas, Wafaa Albarakati, Mouffak Benchohra, Juan J. Trujillo

Arabian Journal of Mathematics > 2016 > 5 > 1 > 1-7

This paper deals with some existence and Ulam stability results for a class of partial integral equations via Hadamard’s fractional integral, by applying Schauder’s fixed-point theorem.

article

Upper and lower solutions method for partial discontinuous fractional differential inclusions with not instantaneous impulses

Saïd Abbas, Mouffak Benchohra, Mohamed Abdalla Darwish

Discussiones Mathematicae, Differential Inclusions, Control and Optimization > 2016 > 36 > 2 > 155-179

In this paper, we use the upper and lower solutions method combined with a fixed point theorem for multivalued maps in Banach algebras due to Dhage for investigations of the existence of solutions of a class of discontinuous partial differential inclusions with not instantaneous impulses. Also, we study the existence of extremal solutions under Lipschitz, Carath´eodory and certain monotonicity conditions

article

Uniqueness and Ulam stabilities results for partial fractional differential equations with not instantaneous impulses

Saïd Abbas, Mouffak Benchohra

Applied Mathematics and Computation > 2015 > 257 > Complete > 190-198

In this paper, we investigate some uniqueness and Ulam’s type stability concepts of fixed point equations for a class of partial functional differential equations with not instantaneous impulses in Banach spaces. An example is also provided to illustrate our results.

article

Upper and lower solutions method for partial Hadamard fractional integral equations and inclusions

Saïd Abbas, Eman Alaidarous, Wafaa Albarakati, Mouffak Benchohra

Discussiones Mathematicae, Differential Inclusions, Control and Optimization > 2015 > 35 > 2 > 105-122

In this paper we use the upper and lower solutions method combined with Schauder's fixed point theorem and a fixed point theorem for condensing multivalued maps due to Martelli to investigate the existence of solutions for some classes of partial Hadamard fractional integral equations and inclusions.

article

New existence and stability results for partial fractional differential inclusions with multiple delay

Saïd Abbas, Wafaa Albarakati, Mouffak Benchohra, Mohamed Darwish, more

Annales Polonici Mathematici > 2015 > 114 > 1 > 81-100

We discuss the existence of solutions and Ulam's type stability concepts for a class of partial functional fractional differential inclusions with noninstantaneous impulses and a nonconvex valued right hand side in Banach spaces. An example is provided to illustrate our results.

article

Existence and Ulam Stability for Partial Impulsive Discontinuous Fractional Differential Inclusions in Banach Algebras

Saïd Abbas, Mouffak Benchohra

Mediterranean Journal of Mathematics > 2015 > 12 > 4 > 1245-1264

In this paper, we investigate some existence and Ulam’s type stability concepts of fixed point inclusions for a class of partial discontinuous fractional-order differential inclusions with impulses in Banach Algebras. Our results are obtained using weakly Picard operators theory.

article

Fractional order integral equations of two independent variables

Saïd Abbas, Mouffak Benchohra

Applied Mathematics and Computation > 2014 > 227 > Complete > 755-761

In this paper, we present some results concerning the existence, the uniqueness and the attractivity of solutions for some functional integral equations of Riemann–Liouville fractional order, by using some fixed point theorems.

article

Ulam–Hyers Stability for the Darboux Problem for Partial Fractional Differential and Integro-differential Equations via Picard Operators

Saïd Abbas, Mouffak Benchohra

Results in Mathematics > 2014 > 65 > 1-2 > 67-79

In the present paper we investigate some uniqueness and Ulam’s type stability concepts of fixed point equations due to Rus, for the Darboux problem of partial differential and integro-differential equations involving the Caputo fractional derivative. Our results are obtained by using weakly Picard operators theory.

article

Existence and attractivity for fractional order integral equations in Fréchet spaces

Saïd Abbas, Mouffak Benchohra

Discussiones Mathematicae, Differential Inclusions, Control and Optimization > 2013 > 33 > 1 > 47-63

In this paper, we present some results concerning the existence and the attractivity of solutions for some functional integral equations of Riemann-Liouville fractional order, by using an extension of the Burton-Kirk fixed point theorem in the case of a Fréchet space.

article

On fractional order derivatives and Darboux problem for implicit differential equations

Saïd Abbas, Mouffak Benchohra, Aleksandr N. Vityuk

Fractional Calculus and Applied Analysis > 2012 > 15 > 2 > 168-182

In this paper we prove some relations between the Riemann-Liouville and the Caputo fractional order derivatives, and we investigate the existence and uniqueness of solutions for the initial value problems (IVP for short), for a class of functional hyperbolic differential equations by using some fixed point theorems.

article

Integro-Differential Equations of Fractional Order

Saïd Abbas, Mouffak Benchohra, John R. Graef

Differential Equations and Dynamical Systems > 2012 > 20 > 2 > 139-148

In this paper, the authors present some results concerning the existence and uniqueness of solutions of an integro-differential equation of fractional order by using Banach’s contraction principle, Schauder’s fixed point theorem, and the nonlinear alternative of Leray–Schauder type.

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INFONA - science communication portal

Search results for: Saïd Abbas

On implicit fractional q‐difference equations: Analysis and stability

The effects of curcumin as dietary supplement for patients with polycystic ovary syndrome: An updated systematic review and meta‐analysis of randomized clinical trials

Existence and Ulam stability for implicit fractional q-difference equations

Caputo–Hadamard fractional differential Cauchy problem in Fréchet spaces

Coupled Hilfer fractional differential systems with random effects

Implicit coupled Hilfer–Hadamard fractional differential systems under weak topologies

A survey on Hadamard and Hilfer fractional differential equations: Analysis and stability

Stability results for partial fractional differential equations with noninstantaneous impulses

Existence and attractivity for the Darboux problem of fractional order neutral differential equations

Ulam stabilities for partial Hadamard fractional integral equations

Upper and lower solutions method for partial discontinuous fractional differential inclusions with not instantaneous impulses

Uniqueness and Ulam stabilities results for partial fractional differential equations with not instantaneous impulses

Upper and lower solutions method for partial Hadamard fractional integral equations and inclusions

New existence and stability results for partial fractional differential inclusions with multiple delay

Existence and Ulam Stability for Partial Impulsive Discontinuous Fractional Differential Inclusions in Banach Algebras

Fractional order integral equations of two independent variables

Ulam–Hyers Stability for the Darboux Problem for Partial Fractional Differential and Integro-differential Equations via Picard Operators

Existence and attractivity for fractional order integral equations in Fréchet spaces

On fractional order derivatives and Darboux problem for implicit differential equations

Integro-Differential Equations of Fractional Order

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