• Journal of applied mathematics & informatics
• /
• 제32권3_4호
• /
• pp.359-375
• /
• 2014

In this paper, a multiobjective nondifferentiable fractional programming problem (MFP) is considered where the objective function contains a term involving the support function of a compact convex set. A vector valued (generalized) ${\alpha}$-univex function is defined to extend the concept of a real valued (generalized) ${\alpha}$-univex function. Using these functions, sufficient optimality criteria are obtained for a feasible solution of (MFP) to be an efficient or weakly efficient solution of (MFP). Duality results are obtained for a Mond-Weir type dual under (generalized) ${\alpha}$-univexity assumptions.

• 대한수학회논문집
• /
• 제36권2호
• /
• pp.267-276
• /
• 2021

The aim of the present investigation is to establish the composition formulas for the pathway fractional integral operator connected with Hurwitz-Lerch zeta function and extended Wright-Bessel function. Some interesting special cases have also been discussed.

• 대한수학회논문집
• /
• 제31권4호
• /
• pp.869-878
• /
• 2016

This paper presents an ecient fractional shifted Legendre polynomial method to solve the fractional Volterra's model for population growth model. The fractional derivatives are described based on the Caputo sense by using Riemann-Liouville fractional integral operator. The theoretical analysis, such as convergence analysis and error bound for the proposed technique has been demonstrated. In applications, the reliability of the technique is demonstrated by the error function based on the accuracy of the approximate solution. The numerical applications have provided the eciency of the method with dierent coecients of the population growth model. Finally, the obtained results reveal that the proposed technique is very convenient and quite accurate to such considered problems.

• Journal of applied mathematics & informatics
• /
• 제33권1_2호
• /
• pp.119-125
• /
• 2015

In this note, two new mappings associated with convexity are propoesd, by which we obtain some new Hermite-Hadamard type inequalities for convex functions via Riemann-Liouville fractional integrals. We conclude that the results obtained in this work are the refinements of the earlier results.

• Kyungpook Mathematical Journal
• /
• 제56권3호
• /
• pp.845-859
• /
• 2016

In this paper, some Hermite-Hadamard-$Fej{\acute{e}}r$ type integral inequalities for harmonically quasi-convex functions in fractional integral forms have been obtained.

• Kyungpook Mathematical Journal
• /
• 제47권4호
• /
• pp.519-527
• /
• 2007

In this paper, we establish a theorem wherein we have obtained the image of modified H-transform under the fractional integral operator involving Foxs H-function. Three corollaries of this theorem have also been derived. Further, we obtain one interesting integral by the application of the third corollary. The importance of above findings lies in the fact that our main theorem involves Fox H-function which is very general in nature. The result obtained earlier by Tariq (1998) is a special case of our main findings.

• 대한수학회논문집
• /
• 제33권2호
• /
• pp.423-436
• /
• 2018

We aim to establish certain Saigo hypergeometric fractional integral formulas for a finite product of the generalized k-Bessel functions, which are also used to present image formulas of several integral transforms including beta transform, Laplace transform, and Whittaker transform. The results presented here are potentially useful, and, being very general, can yield a large number of special cases, only two of which are explicitly demonstrated.

• East Asian mathematical journal
• /
• 제18권1호
• /
• pp.111-125
• /
• 2002

Many different families of infinite series were recently observed to be summable in closed forms by means of certain operators of fractional calculus(that is, calculus of integrals and derivatives of any arbitrary real or complex order). In this sequel to some of these recent investigations, the authors present yet another instance of applications of certain fractional calculus operators. Alternative derivations without using these fractional calculus operators are shown to lead naturally a family of analogous infinite sums involving hypergeometric functions.

• Korean Journal of Mathematics
• /
• 제6권2호
• /
• pp.183-194
• /
• 1998

Making use of a certain operator of fractional derivative, a new subclass $L_p({\alpha},{\beta},{\gamma},{\lambda})$) of analytic and p-valent functions is introduced in the present paper. Apart from various coefficient bounds, many interesting and useful properties of this class of functions are given, some of these properties involve, for example, linear combinations and modified Hadamard product of several functions belonging to the class introduced here.

• Journal of applied mathematics & informatics
• /
• 제31권5_6호
• /
• pp.853-867
• /
• 2013

In this paper a methodology is developed to solve a nonlinear fractional programming problem, whose objective function and constraints are interval valued functions. Interval valued convex fractional programming problem is studied. This model is transformed to a general convex programming problem and relation between the original problem and the transformed problem is established. These theoretical developments are illustrated through a numerical example.