Browsing by Author "Nasim, C."

Now showing 1 - 11 of 11
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    An operational procedure for Hankel type integrals
    (1987-01-01) Nasim, C.
    In this paper, an operational procedure is established to evaluate Hankel type integrals. First, an operator L(θ), θ≡−xddx is constructed, which defines the integral. Then making use of some basic properties of this operator, an elementary procedure is developed for evaluating integrals for a special class of analytic functions. A few example are given to illustrate the technique.
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    Dual integral equations involving Weber-Orr transforms
    (1991-01-01) Nasim, C.
    In this paper we consider dual integral equations involving inverseWeber-Orr transforms of the type Wν−k,ν−1[;], k=0,1,…. A general solution isestablished using elementary methods. Many known results are derived as special cases.
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    Inversion of the Poisson-Hankel transform
    (1982-01-01) Nasim, C.
    The Poisson-Hankel transform is defined as an integral transform of the initial temperature function, with the kernel as the source solution of the generalized heat equation. In this paper a technique involving integral and differential operators has been used to effect the inversion of the Poisson-Hankel transform.
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    On -transform
    (1981-01-01) Nasim, C.
    Using a combination of infinite order linear differential operators and integral operators, the inversion of K-transform is established. Inversion procedures for Laplace transform and Potential transform are derived as special cases.
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    On a generalization of Hankel kernel
    (1994-01-01) Nasim, C.; Aggarwala, B. D.
    We consider an expression involving the Bessel function, the Neumann function and the MacDonald function and discover various combinations of these functions which are Fourier kernels or conjugate Fourier kernels. Also a large number of integration formulae are established involving these kernels.
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    On dual integral equations arising in problems of bending of anisotropic plates
    (1992-01-01) Aggarwala, B. D.; Nasim, C.
    In this paper we consider dual integral equations, which arise in boundary value problems of bending of anisotropic plates. The function involved in these equations is a linear combination of elementary function, which turns out to be a particular case of a class of Fourier kernels, [2]. The method used here for solving the equations is some what similar to the method used for solving dual integral equations of Titchmarsh type, [1].
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    On dual integral equations with Hankel kernel and an arbitrary weight function
    (1986-01-01) Nasim, C.
    In this paper we deal with dual integral equations with an arbitrary weight function and Hankel kernels of distinct and general order. We propose an operational procedure, which depends on exploiting the properties of the Mellin transforms, and readily reduces the dual equations to a single equation. This then can be inverted by the Hankel inversion to give us an equation of Fredholm type, involving the unknown function. Most of the known results are then derived as special cases of our general result.
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    On generalized heat polynomials
    (1988-01-01) Nasim, C.
    We consider the generalized heat equation of nth order ∂2u∂r2+n−1r∂u∂r−α2r2u=∂u∂t. If the initial temperature is an even power function, then the heat transform with the source solution as the kernel gives the heat polynomial. We discuss various properties of the heat polynomial and its Appell transform. Also, we give series representation of the heat transform when the initial temperature is a power function.
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    On the solution of reaction-diffusion equations with double diffusivity
    (1987-01-01) Aggarwala, B. D.; Nasim, C.
    In this paper, solution of a pair of Coupled Partial Differential equations is derived. These equations arise in the solution of problems of flow of homogeneous liquids in fissured rocks and heat conduction involving two temperatures. These equations have been considered by Hill and Aifantis, but the technique we use appears to be simpler and more direct, and some new results are derived. Also, discussion about the propagation of initial discontinuities is given and illustrated with graphs of some special cases.
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    Solutions of an ordinary differential equation as a class of Fourier kernels
    (1990-01-01) Aggarwala, B.; Nasim, C.
    While there are various methods of generating Fourier kernels mentioned in the literature it is not so well recognized that Fourier kernels can be obtained as solutions of differential equations. In this note we define a class of Fourier kernels, which are solutions of a k - fold Bessel equation.
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    Steady state temperatures in a quarter plane
    (1996-01-01) Aggarwala, B. D.; Nasim, C.
    The discontinuous boundary value problem of steady state temperatures in aquarter plane gives rise to a pair of dual integral equations which are not of Titchmarchtype. These dual integral equations are considered in this paper.