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DECOMPOSITION FOR CARTAN’S SECOND CURVATURE TENSOR OF DIFFERENT ORDER IN FINSLER SPACES
Alaa A. Abdallah,A. A. Navlekar,Kirtiwant P. Ghadle,Ahmed A. Hamoud 경남대학교 기초과학연구소 2022 Nonlinear Functional Analysis and Applications Vol.27 No.2
The Cartan’s second curvature tensor P^i_{jkh} is a positively homogeneous of degree-1 in y^i, where yi represent a directional coordinate for the line element in Finsler space. In this paper, we discuss the decomposition of Cartan’s second curvature tensor P^i_{jkh} in two spaces, a generalized BP-recurrent space and generalized BP-birecurrent space. We obtain different tensors which satisfy the recurrence and birecurrence property under the decomposition. Also, we prove the decomposition for different tensors are non-vanishing. As an illustration of the applicability of the obtained results, we finish this work with some illustrative examples.
APPROXIMATE SOLUTION OF FRACTIONAL BLACK-SCHOLE’S EUROPEAN OPTION PRICING EQUATION BY USING ETHPM
Pradip R. Bhadane,KIRTIWANT P. GHADLE,AHMED A. HAMOUD 경남대학교 기초과학연구소 2020 Nonlinear Functional Analysis and Applications Vol.25 No.2
We proposed a new reliable combination of new Homotopy Perturbation Method(HPM) and Elzaki transform called as Elzaki Transform Homotopy Perturbation Method(ETHPM) is designed to obtain a exact solution to the fractional Black-Scholes equationwith boundary condition for a European option pricing problem. The fractional derivativeis in Caputo sense and the nonlinear terms in Fractional Black-Scholes Equation can behandled by using HPM. The Black-Scholes formula is used as a model for valuing Europeanor American call and put options on a non-dividend paying stock. The methods give ananalytic solution of the fractional Black-Scholes equation in the form of a convergent series. Finally, some examples are included to demonstrate the validity and applicability of theproposed technique.
SOLVING FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS BY USING NUMERICAL TECHNIQUES
Hamoud Ahmed A.,Hussain Khawlah H.,Mohammed Nedal M.,Ghadle Kirtiwant P. 경남대학교 기초과학연구소 2019 Nonlinear Functional Analysis and Applications Vol.24 No.3
This paper mainly focuses on numerical techniques based on the Adomian Decomposition Method (ADM) and Direct Homotopy Analysis Method (DHAM) for solving Fredholm integro-differential equations of the second kind. The reliability of the methods and reduction in the size of the computational work give this methods wider applicability. Convergence analysis of the exact solution of the proposed methods will be established. Moreover, we proved the uniqueness of the solution. To illustrate the methods, an example is presented.
Ahmed A. Hamoud,Nedal M. Mohammed,Homan Emadifar,Faraidum K. Hamasalh,Soubhagya Kumar Sahoo,Masoumeh Khademi,Foroud Parvaneh 한국지능시스템학회 2022 INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGE Vol.22 No.4
In this paper, we established some new results concerning the existence and uniquenessof the solutions of nonlinear Atangana-Baleanu-Caputo fractional (ABC-fractional) FuzzyVolterra-Fredholm integro-differential equations. These new findings are obtained using thetheorems of a fixed point. In addition, we investigate Hyers-Ulam stability for this fractionalsystem. Our work extends and improves the results in the literature. Finally, some examplesdemonstrate the validity of the obtained theoretical results.
THE RELIABLE MODIFIED OF ADOMIAN DECOMPOSITION METHOD FOR SOLVING INTEGRO-DIFFERENTIAL EQUATIONS
Hamoud, Ahmed A.,Ghadle, Kirtiwant P. Chungcheong Mathematical Society 2019 충청수학회지 Vol.32 No.4
In this article, we discussed semi-analytical approximated methods for solving mixed Volterra-Fredholm integro-differential equations, namely: Adomian decomposition method and modified Adomian decomposition method. Moreover, we prove the uniqueness results and convergence of the techniques. Finally, an example is included to demonstrate the validity and applicability of the proposed techniques.
THE RELIABLE MODIFIED OF ADOMIAN DECOMPOSITION METHOD FOR SOLVING INTEGRO-DIFFERENTIAL EQUATIONS
Ahmed A,Hamoud,Kirtiwant P,Ghadle 충청수학회 2019 충청수학회지 Vol.32 No.4
In this article, we discussed semi-analytical approximated methods for solving mixed Volterra-Fredholm integro-differential equations, namely: Adomian decomposition method and modified Adomian decomposition method. Moreover, we prove the unique-ness results and convergence of the techniques. Finally, an example is included to demonstrate the validity and applicability of the proposed techniques.
EXISTENCE AND UNIQUENESS RESULTS FOR NONLINEAR VOLTERRA-FREDHOLM INTEGRO DIFFERENTIAL EQUATIONS
Ahmed A. Hamoud,M.SH. Bani Issa,KIRTIWANT P. GHADLE 경남대학교 기초과학연구소 2018 Nonlinear Functional Analysis and Applications Vol.23 No.4
In this article, variational iteration technique is successfully applies to find the approximate solutions of nonlinear Volterra-Fredholm integro-differential equations. The reliability of the method and reduction in the size of the computational work give this method a wider applicability. Moreover, we prove the existence and uniqueness results. Finally, the examples are included to demonstrate the validity and applicability of the proposed technique.
Ahmed A. Hamoud,KIRTIWANT P. GHADLE 강원경기수학회 2017 한국수학논문집 Vol.25 No.3
In this paper, we propose a combined form for solving nonlinear interval Volterra-Fredholm integral equations of the second kind based on the modifying Laplace Adomian decomposition method. We find the exact solutions of nonlinear interval Volterra-Fredholm integral equations with less computation as compared with standard decomposition method. Finally, an illustrative example has been solved to show the efficiency of the proposed method.
The reliable modified of Adomian decomposition method for Solving Integro-Differential Equations
AHMED A. HAMOUD,KIRTIWANT P. GHADLE 충청수학회 2019 충청수학회지 Vol.32 No.4
'In this article, we discussed semi-analytical approximated methods for solving mixed Volterra-Fredholm integro-differential equations, namely: Adomian decomposition method and modified Adomian decomposition method. Moreover, we prove the uniqueness results and convergence of the techniques. Finally, an example is included to demonstrate the validity and applicability of the proposed techniques.
EXISTENCE AND UNIQUENESS RESULTS FOR CAPUTO FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS
AHMED A. HAMOUD,MOHAMMED. S. ABDO,KIRTIWANT P. GHADLE 한국산업응용수학회 2018 Journal of the Korean Society for Industrial and A Vol.22 No.3
This paper successfully applies the modified Adomian decomposition method to find the approximate solutions of the Caputo fractional integro-differential equations. The reliability of the method and reduction in the size of the computational work give this method a wider applicability. Also,the behavior of the solution can be formally determined by analytical approximation. Moreover, we proved the existence and uniqueness results and convergence of the solution. Finally,an example is included to demonstrate the validity and applicability of the proposed technique.