Title: Optimality and Duality Defined by the Concept of Tempered Fractional Univex Functions in Multi-Objective Optimization
Author(s): Rabha W. Ibrahim
Pages: 75-85
Cite as:
Rabha W. Ibrahim, Optimality and Duality Defined by the Concept of Tempered Fractional Univex Functions in Multi-Objective Optimization, Int. J. Anal. Appl., 15 (1) (2017), 75-85.

Abstract


In this paper, we purpose the concept of tempered Univex functions by utilizing a tempered fractional difference-differential operator type Caputo. This instruction indicates a new class of these functions in some optimal problems by exemplifying the settings on the modified formula. We call it the class of tempered fractional Univex functions. Our study is based on the strong, weak, converse, and strict converse duality propositions. A Multi-objective optimal problem includes the new process is disentangled.

Full Text: PDF

 

References


  1. C.F. Dunkl, Differential-difference operators associated to reflection groups, Trans. Amer. Math. Soc. 311 (1) (1989), 167–183.

  2. M. Rosler and M. Voit, Markov processes related with Dunkl operators. Adv. Appl. Math. 21(4)(1998) 575–643.

  3. R. W. Ibrahim, New classes of analytic functions determined by a modified differential-difference operator in a complex domain, Karbala Int. J. Modern Sci. 3 (2017) 53–58.

  4. K.S. Miller, B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wily& Sons (1993).

  5. A.A. Kilbas, H.M. Srivastava, J.J. Trujiilo, Theory and Applications of Fractional Differential Equations. Amsterdam, Netherlands: Elsevier (2006).

  6. B. Baeumer, M.M. Meerschaert, Tempered stable Levy motion and transient super-diffusion, J. Comput. Appl. Math. 233 (2010) 243–2448.

  7. R. W. Ibrahim, Fractional calculus of Multi-objective functions & Multi-agent systems. LAMBERT Academic Publishing, Saarbrcken, Germany 2017.

  8. V.E. Tarasov, Leibniz rule and fractional derivatives of power functions. J. Comput. Nonlinear Dyn. 11 (3) (2016), Art. ID 031014–4.