The Journal of the Indian Mathematical Society

Deshna Loonker ¹, P. K. Banerji ¹

Affiliations
1 Department of Mathematics, Faculty of Science, J. N. V. University, Jodhpur - 342 005, IN

Abstract

In this paper Elzaki transform is defined for distribution spaces. Solution of the Abel integral equation is obtained using distributional Elzaki transform is proved in distributional sense. The fractional integral and derivatives (as form of the integral equation) is also employed on distribution spaces.

Keywords

Elzaki Transform, Laplace Transform, Abel Integral Equation, Distribution Spaces, Fractional Integrals and Derivatives.

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P. L. Sethi ¹, P. K. Banerji ¹

Affiliations
1 Department of Mathematics, University of Jodhpur, Jodhpur, IN

Abstract

Following a method of fractional integration operators, we have presented a formal solution of the set of dual integral equations involving the ordinary Bessel function.

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P. K. Banerji ¹, G. M. Shenan ¹

Affiliations
1 Department of Mathematics, JNV University, Jodhpur-342005, IN

Abstract

In the present paper a function is introduced using certain modified fractional derivative operator and the convolutions of three functions, analytic in the unit disc, are mentioned. Also investigated are the characterization properties of the said function in the open unit disc, in order to establish its belongingness to some subclasses of analytic functions and finally, some associations of the said properties with the convolution are mentioned.

Keywords

Convex Functions, Starlike Functions, Fractional Derivative Operator, Convolution.

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P. K. Banerji ¹, M. G. Binsaad ², F. B. F. Mohsen ¹

Affiliations
1 Department o f Mathematics, J.N.V. University, Jodhpur-342 005, IN
2 Department of Mathematics, University of Aden, Aden, YE

Abstract

In this paper we apply the concept of Nishimoto’s fractional calculus (N-fractional calculus) to obtain some linear, bilinear and bilateral generating functions involving hypergeometric functions of two and three variables. Some particular cases are mentioned too.

Keywords

Generating Functions, Hypergeometric Functions, Appell’s Functions, Lauricella’s Functions, Fractional Derivative.

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S. B. Joshi ¹, P. K. Banerji ²

Affiliations
1 Department of Mathematics, Walchand College of Engineering, Sangli-416 415, IN
2 Department of Mathematics, J.N.V. University, Jodhpur-342 005, IN

Abstract

For certain class of functions analytic in the unit disk and by employing Ruscheweyh derivative of certain order, some inequalties for specific multivalent functions have been established and appeal to be much general in nature than the ones found earlier.

Keywords

Ruscheweyh Derivative, Convolution, Multivalent Function.

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