Reza Arab
@iausari.ac.ir
Department of Mathematics
Islamic Azad University - Sari
Scopus Publications
Scholar Citations
Scholar h-index
Scholar i10-index
Scopus Publications
M. Mursaleen, S. M. H. Rizvi, R. Arab, A. S. Haghighi, and R. Allahyari
Springer Science and Business Media LLC
Reza Arab and Mohsen Rabbani
Rocky Mountain Mathematics Consortium
A new measure of noncompactness (Mnc) and Darbo fixed point theorem are utilized on space L(R+) to prove the existence of solution for functional Volterra-Fredholm integral equations. An example is given to confirm the validity of results. Furthermore, we propound an iterative algorithm by Sinc interpolation to find the solution with an acceptable accuracy. In this algorithm, it does not need the problem is discretized to an algebraic system with unknown coefficients and we have an iterative processes to aproximate of solution with exponential convergence.
Bipan Hazarika, Mohsen Rabbani, Ravi P. Agarwal, Anupam Das, and Reza Arab
Springer Science and Business Media LLC
In this article, solvability of infinite system of nonlinear singular integral equations of two variables in Banach sequence spaces $$c_{0}$$ c 0 and $$\\ell _{1}$$ ℓ 1 is investigated. For this purpose, Hausdorff measure of noncompactness (in short, Hausdorff MNC) and Meir–Keeler condensing operators are employed. The guarantee of our results are given by some examples. Also to approach an approximation of semi-analytic solution, we introduce a coupled modified homotopy perturbation and Adomian decomposition method. Thus, an iterative algorithm is constructed to find the above solution. The numerical results show that the produced sequence to approximate the solution has a high accuracy.
Hemant Kumar Nashine, Reza Arab, and Rabha W. Ibrahim
World Scientific Pub Co Pte Lt
In this paper, we create tripled fixed point outcomes via a subjective measure of noncompactness in the sense of Banas and Goebel. Furthermore, we introduce some applications of the measure of noncompactness notion to functional equations including nonlinear integral equations as well as local fractional integral equations.
Hemant Kumar Nashine, Reza Arab, and Rabha W. Ibrahim
Springer Singapore
Hemant Kumar Nashine, Rabha W. Ibrahim, Reza Arab, and M. Rabbani
Springer Singapore
Hemant Kumar Nashine, Reza Arab, Pradip R. Patle, and Deepesh Kumar Patel
Informa UK Limited
Reza Arab, Hemant Kumar Nashine, N. H. Can, and Tran Thanh Binh
Springer Science and Business Media LLC
AbstractWe investigate the solutions of functional-integral equation of fractional order in the setting of a measure of noncompactness on real-valued bounded and continuous Banach space. We introduce a new μ-set contraction operator and derive generalized Darbo fixed point results using an arbitrary measure of noncompactness in Banach spaces. An illustration is given in support of the solution of a functional-integral equation of fractional order.
Mohsen Rabbani, Anupam Das, Bipan Hazarika, and Reza Arab
Elsevier BV
Abstract The purpose of this article is to introduce a new tempered sequence space and obtain the measure of noncompactness in this space. Using the measure of noncompactness and generalized Darbo fixed point theorem, we discuss the existence of solutions of an infinite system of fractional differential equations. Also we provide an example to highlight and establish the importance of our main result. Finally, we approach the solution of the example with high accuracy, by a convergent iterative algorithm with the help of modified homotopy perturbation method.
Pradip Ramesh Patle, Deepesh Kumar Patel, and Reza Arab
Springer Science and Business Media LLC
Primarily this work intends to prove the best proximity point (pair) results using the concept of measure of noncompactness and simulation functions. The obtained results generalize and extend some present state of the art on Darbo type fixed point theorems. The main results are applied to actualize the optimum solutions of a system of nonlinear mixed Fredholm–Volterra functional integro-differential equations with local initial conditions.
Mohsen Rabbani, Anupam Das, Bipan Hazarika, and Reza Arab
Elsevier BV
Abstract In this article, we establish the existence of solution for two dimensional nonlinear fractional integral equation using fixed point theorem and measure of noncompactness. Applicability of our results is shown by some examples and for validity of the proposed method we make an iterative algorithm by semi-analytic technique that finds a closed form of the solution with an acceptable accuracy. Ability of the proposed method is granted by comparison with another method found in existing literature.
Reza Allahyari, Reza Arab, and Ali Shole Haghighi
Mathematical Notes
Hemant Kumar Nashine, Rabha W. Ibrahim, Reza Arab, and Mohsen Rabbani
Vilnius University Press
Fractional dynamics is a scope of study in science considering the action of systems. These systems are designated by utilizing derivatives of arbitrary orders. In this effort, we discuss the sufficient conditions for the existence of the mild solution (m-solution) of a class of fractional dynamic systems (FDS). We deal with a new family of fractional m-solution in Rn for fractional dynamic systems. To accomplish it, we introduce first the concept of (F, ψ)-contraction based on the measure of noncompactness in some Banach spaces. Consequently, we establish requisite fixed point theorems (FPTs), which extend existing results following the Krasnoselskii FPT and coupled fixed point results as a outcomes of derived one. Finally, we give a numerical example to verify the considered FDS, and we solve it by iterative algorithm constructed by semianalytic method with high accuracy. The solution can be considered as bacterial growth system when the time interval is large.
Bipan Hazarika, Reza Arab, and M. Mursaleen
Springer Science and Business Media LLC
The objective of this paper is to study the existence of solution of functional integral equations using a measure of noncompactness argument combined with generalized coupled fixed point theorem with the help of operator type contraction mapping in Banach spaces. We present an example to illustrate our results.
Bipan Hazarika, H.M. Srivastava, Reza Arab, and Mohsen Rabbani
Elsevier BV
Abstract The aim of this article is to investigate the existence of solution for the nonlinear functional integral equations with the help of measure of noncompactness, simulation function and generalized Darbo fixed point theorem. Also we provided example for the applicability of obtained results to the theory of integral equations. Also we introduce an iteration algorithm by modified homotopy perturbation and Adomian decomposition method to find solution of the above problem with high accuracy. Finally we have a discussion about convergence and upper bound of error.
Reza Arab, Mohammad Mursaleen, and Syed M. H. Rizvi
Informa UK Limited
Abstract The objective of this article is to establish a fixed point theorem using different class of control functions, which is a generalization of Darbo’s fixed point theorem (DFPT) and its various versions obtained by several authors. Using this result we obtain existence of at least one positive solution for a quadratic integral equation of Fredholm type.
Mohsen Rabbani, Reza Arab, and Bipan Hazarika
Elsevier BV
Abstract The aim of this article is to prove the existence of solution for nonlinear quadratic integral equations using the generalized form of Darbo fixed point theorem with the help of measure of noncompactness and simulation type condensing operator in the Banach space L2[0, 1]. To illustrate validity of the analytical results, we present a nonlinear integral equation as an application. Finally, we introduce an iteration algorithm by modified homotopy perturbation and Adomian decomposition method to find solution of the above problem with a high accuracy.
Anupam Das, Bipan Hazarika, Reza Arab, and M. Mursaleen
Springer Science and Business Media LLC
In this article, we establish some generalization of Darbo type coupled fixed point theorem and give some results on the existence of solutions for a system of nonlinear functional integral equations in Banach space. We illustrated the results with the help of an example.
Bipan Hazarika, Reza Arab, and Poom Kumam
Springer Science and Business Media LLC
In this paper we study some coupled fixed point theorems and coupled coincidence fixed point theorems for infinite family mappings satisfying different contractive conditions on the complete partially ordered metric space with the help of concept of mixed g-monotone property. Further we used generalized Darbo type coupled fixed point theorem to find the existence of solutions for a system of nonlinear functional integral equations in Banach space with the help of measure of noncompactness.
Bipan Hazarika, Reza Arab, and M. Mursaleen
National Library of Serbia
The aim of this paper is to obtain existence results for an infinite system of second order differential equations in the sequence space lp for 1 ? p < ? with the help of a technique associated with measures of noncompactness and contractive condition of operator type. We also provide some illustrative examples in support of our existence theorems.