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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 수학교육과 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.
KIRTIWANT P. GHADLE,ABHIJEET B. ADHE 한국산업응용수학회 2020 Journal of the Korean Society for Industrial and A Vol.24 No.1
The concept of temperature distribution in inhomogeneous semi-infinite solids is examined by making use of direct integration method. The analysis is done on the solution of the in-plane steady state heat conduction problem under certain boundary conditions. The method of direct integration has been employed, which is then reduced to Volterra integral equation of second kind, produces the explicit form analytical solution. Using resolvent- kernel algorithm, the governing equation is solved to get present solution. The temperature distribution obtained and calculated numerically and the relation with distribution of heat flux generated by internal heat source is shown graphically.
FIRDOUS KHAN,KIRTIWANT P. GHADLE 한국산업응용수학회 2019 Journal of the Korean Society for Industrial and A Vol.23 No.3
In this article, a systematic solution based on the sequence of expansion method is planned to solve the time-fractional diffusion equation, time-fractional telegraphic equation and time-fractional wave equation in three dimensions using a current and valid approximate method, namely the ADM, VIM, and the NIM subject to the estimate initial condition. By using these three methods it is likely to find the exact solutions or a nearby approximate solution of fractional partial differential equations. The exactness, efficiency, and convergence of the method are demonstrated through the three numerical examples.
SOLVING FUZZY FRACTIONAL WAVE EQUATION BY THE VARIATIONAL ITERATION METHOD IN FLUID MECHANICS
FIRDOUS KHAN,KIRTIWANT P. GHADLE 한국산업응용수학회 2019 Journal of the Korean Society for Industrial and A Vol.23 No.4
In this paper, we are extending fractional partial differential equations to fuzzy fractional partial differential equation under Riemann-Liouville and Caputo fractional derivatives, namely Variational iteration methods, and this method have applied to the fuzzy fractional wave equation with initial conditions as in fuzzy. It is explained by one and two-dimensional wave equations with suitable fuzzy initial conditions.
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.
APPROXIMATE SOLUTION OF FRACTIONAL BLACK-SCHOLE’S EUROPEAN OPTION PRICING EQUATION BY USING ETHPM
Pradip R. Bhadane,KIRTIWANT P. GHADLE,AHMED A. HAMOUD 경남대학교 수학교육과 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.
DIFFERENTIAL INCLUSIONS OF FRACTIONAL ORDER WITH IMPULSE EFFECTS IN BANACH SPACES
NAWAL A. ALSARORI,KIRTIWANT P. GHADLE 경남대학교 수학교육과 2020 Nonlinear Functional Analysis and Applications Vol.25 No.1
Impulsive fractional semilinear differential inclusions in Banach spaces are considered. We investigate the situation when the linear part generates a semigroup not required to be compact and the multivalued function is lower semicontinuous and nonconvex. Our result are obtained by using noncompactness Hausdorff measure (NCHM), multivalued properties and fixed point theorems. We finally present an example to lighten our 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.
QUASI-STATIC THERMOELASTIC PROBLEM OF AN INFINITELY LONG CIRCULAR CYLINDER
KISHOR R. GAIKWAD,KIRTIWANT P. GHADLE 한국산업응용수학회 2010 Journal of the Korean Society for Industrial and A Vol.14 No.3
The aim of this work is to determine the quasi-static thermal stresses of an in-finitely long circular cylinder having constant initial temperature under steady-state field. The arbitrary heat flux is applied on the lower surface and the upper surface of the cylinder is at initial temperature. The fixed circular edge is thermally insulated. The results are obtained in series form in terms of Bessel’s functions. These have been computed numerically and illustrated graphically.
NONLOCAL FRACTIONAL DIFFERENTIAL INCLUSIONS WITH IMPULSE EFFECTS AND DELAY
NAWAL A. ALSARORI,KIRTIWANT P. GHADLE 한국산업응용수학회 2020 Journal of the Korean Society for Industrial and A Vol.24 No.2
Functional fractional differential inclusions with impulse effects in general Banach spaces are studied. We discuss the situation when the semigroup generated by the linear part is equicontinuous and the multifunction is Caratheodory. First, we define the PC-mild solutions for functional fractional semilinear impulsive differential inclusions. We then prove the existence of PC-mild solutions for such inclusions by using the fixed point theorem, multivalued properties and applications of NCHM (noncompactness Hausdorff measure). Eventually, we enhance the acquired results by giving an example.