• Journal of applied mathematics & informatics
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• v.37 no.5_6
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• pp.341-349
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• 2019

This paper is concerned to investigate M-Wright function, which was earlier known as transcendental function of the Wright type. M-Wright function is a special case of the Wright function given by British mathematician (E.Maitland Wright) in 1933. We have explored the cosequences of Riemann-Liouville Integral and Differential operators on M-Wright function. We have also evaluated integral transforms of the M-Wright function.

• East Asian mathematical journal
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• v.21 no.2
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• pp.191-203
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• 2005

In the present paper we first establish some basic results for a substantially more general class of functions defined below. The results include simple differentiation and fractional calculus operators(integration and differentiation of arbitrary orders) for this class of functions. These results are then invoked in determining similar properties for the generalized Wright's hypergeometric functions. Further, norm estimate of a certain class of integral operators whose kernel involves the generalized Wright's hypergeometric function, and its composition(and other related properties) with the fractional calculus operators are also investigated.

• Communications of the Korean Mathematical Society
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• v.37 no.3
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• pp.681-692
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• 2022

Special functions and Geometric function theory are close related to each other due to the surprise use of hypergeometric function in the solution of the Bieberbach conjecture. The purpose of this paper is to provide a set of sufficient conditions under which the normalized four parametric Wright function has lower bounds for the ratios to its partial sums and as well as for their derivatives. The sufficient conditions are also obtained by using Alexander transform. The results of this paper are generalized and also improved the work of M. Din et al. [15]. Some examples are also discussed for the sake of better understanding of this article.

• Journal of applied mathematics & informatics
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• v.34 no.3_4
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• pp.249-255
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• 2016

The object of the present paper is to establish two interesting unified integral formulas involving Multiple (multiindex) Mittag-Leffler functions, which is expressed in terms of Wright hypergeometric function. Some deduction from these results are also considered.

• Bulletin of the Korean Mathematical Society
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• v.51 no.4
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• pp.995-1003
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• 2014

A remarkably large number of integral formulas involving a variety of special functions have been developed by many authors. Also many integral formulas involving various Bessel functions have been presented. Very recently, Choi and Agarwal derived two generalized integral formulas associated with the Bessel function $J_{\nu}(z)$ of the first kind, which are expressed in terms of the generalized (Wright) hypergeometric functions. In the present sequel to Choi and Agarwal's work, here, in this paper, we establish two new integral formulas involving the generalized Bessel functions, which are also expressed in terms of the generalized (Wright) hypergeometric functions. Some interesting special cases of our two main results are presented. We also point out that the results presented here, being of general character, are easily reducible to yield many diverse new and known integral formulas involving simpler functions.

• Honam Mathematical Journal
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• v.39 no.3
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• pp.349-361
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• 2017

By means of the Oberhettinger integral, certain generalized integral formulae involving product of generalized k-Bessel function $w^{{\gamma},{\alpha}}_{k,v,b,c}(z)$ and general class of polynomials $S^m_n[x]$ are derived, the results of which are expressed in terms of the generalized Wright hypergeometric functions. Several new results are also obtained from the integrals presented in this paper.

• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.755-772
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• 2023

Our aim is to establish certain image formulas of the (p, q)-extended modified Bessel function of the second kind M_ν,p,q(z) by employing the Marichev-Saigo-Maeda fractional calculus (integral and differential) operators including their composition formulas and using certain integral transforms involving (p, q)-extended modified Bessel function of the second kind M_ν,p,q(z). Corresponding assertions for the Saigo's, Riemann-Liouville (R-L) and Erdélyi-Kober (E-K) fractional integral and differential operators are deduced. All the results are represented in terms of the Hadamard product of the (p, q)-extended modified Bessel function of the second kind M_ν,p,q(z) and Fox-Wright function _rΨ_s(z).

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.167-178
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• 2007

This paper deals with the solutions of linear inhomogeneous time-fractional partial differential equations in applied mathematics and fluid mechanics. The fractional derivatives are described in the Caputo sense. The fractional Green function method is used to obtain solutions for time-fractional wave equation, linearized time-fractional Burgers equation, and linear time-fractional KdV equation. The new approach introduces a promising tool for solving fractional partial differential equations.

• Biomaterials and Biomechanics in Bioengineering
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• v.3 no.1
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• pp.47-57
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• 2016

Results from multiple high profile experiments on the parameters influencing the impacts that cause skull fractures to the frontal, temporal, and parietal bones were gathered and analyzed. The location of the impact as a binary function of frontal or lateral strike, the velocity, the striking area of the impactor, and the force needed to cause skull fracture in each experiment were subjected to statistical analysis using the JMP statistical software pack. A novel neural network model predicting skull fracture threshold was developed with a high statistical correlation ($R^2=0.978$) and presented in this text. Despite variation within individual studies, the equation herein proposes a 3 kN greater resistance to fracture for the frontal bone when compared to the temporoparietal bones. Additionally, impacts with low velocities (<4.1 m/s) were more prone to cause fracture in the lateral regions of the skull when compared to similar velocity frontal impacts. Conversely, higher velocity impacts (>4.1 m/s) showed a greater frontal sensitivity.

• Kyungpook Mathematical Journal
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• v.56 no.2
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• pp.597-610
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• 2016

For a sufficiently adequate special case of the Dziok-Srivastava linear operator defined by means of the Hadamard product (or convolution) with Srivastava-Wright convolution operator, the authors investigate several mapping properties involving various subclasses of analytic and univalent functions, $G({\lambda},{\alpha})$ and $M({\lambda},{\alpha})$. Furthermore we discuss some inclusion relations for these subclasses to be in the classes of k-uniformly convex and k-starlike functions.