Paper's Title:

Fractional exp(-φ(ξ))- Expansion Method and its Application to Space--Time Nonlinear Fractional Equations

Author(s):

A. A. Moussa and L. A. Alhakim

Department of Management Information System and Production Management,
College of Business and Economics, Qassim University,
P.O. BOX 6666, Buraidah: 51452,
Saudi Arabia.
E-mail: Alaamath81@gmail.com
URL: https://scholar.google.com/citations?user=ccztZdsAAAAJ&hl=ar

Department of Management Information System and Production Management,
College of Business and Economics, Qassim University,
P.O. BOX 6666, Buraidah: 51452,
Saudi Arabia.
E-mail: Lama2736@gmail.com
URL: https://scholar.google.com/citations?user=OSiSh1AAAAAJ&hl=ar

Abstract:

In this paper, we mainly suggest a new method that depends on the fractional derivative proposed by Katugampola for solving nonlinear fractional partial differential equations. Using this method, we obtained numerous useful and surprising solutions for the space--time fractional nonlinear Whitham--Broer--Kaup equations and space--time fractional generalized nonlinear Hirota--Satsuma coupled KdV equations. The solutions obtained varied between hyperbolic, trigonometric, and rational functions, and we hope those interested in the real-life applications of the previous two equations will find this approach useful.

Paper's Title:

On a Class of Meromorphic Functions of Janowski Type Related with a Convolution Operator

Author(s):

Abdul Rahman S. Juma, Husamaldin I. Dhayea

Department of Mathematics,
Alanbar University, Ramadi,
Iraq.
E-mail: dr_juma@hotmail.com

Department of Mathematics,
Tikrit University, Tikrit,
Iraq.
URL: husamaddin@gmail.com

Abstract:

In this paper, we have introduced and studied new operator $Q^k_λ,m,γ by the Hadamard product (or convolution) of two linear operators D^k_λ and I_m,γ, then using this operator to study and investigate a new subclass of meromorphic functions of Janowski type, giving the coefficient bounds, a sufficient condition for a function to belong to the considered class and also a convolution property. The results presented provide generalizations of results given in earlier works.

Paper's Title:

Preserver of Local Spectrum of Skew-product Operators

Author(s):

Rohollah Parvinianzadeh^1,*, Meysam Asadipour² and Jumakhan Pazhman³

¹Department of Mathematics,
College of Sciences,
University of Yasouj,
Yasouj, 75918-74934,
Iran.
E-mail: r.parvinian@yu.ac.ir

²Department of Mathematics,
College of Sciences,
University of Yasouj,
Yasouj, 75918-74934,
Iran.
E-mail: Asadipour@yu.ac.ir

³Department of Mathematics,
Ghor Institute of higher education,
Afghanistan.
E-mail: jumapazhman@gmail.com

Abstract:

Let H and K be infinite-dimensional complex Hilbert spaces, and B(H) (resp. B(K)) be the algebra of all bounded linear operators on H (resp. on K). For an operator T∈ B(H) and a vector h∈ H, let σ_T(h) denote the local spectrum of T at h. For two nonzero vectors h₀∈ H and k₀∈ K, we show that if two maps φ₁ and φ₂ from B(H) into B(K) satisfy

σ_{φ1(T)φ2(S)*}(k₀)= σ_TS*(h₀})

for all T, S ∈ B(H), and their range containing all operators of rank at most two, then there exist bijective linear maps P : H→ K and Q : K→ H such that φ₁(T) = PTQ and φ₂(T)^* =Q^-1T^*P^-1 for all T ∈ B(H). Also, we obtain some interesting results in this direction.

Paper's Title:

Optimization Techniques on Affine Differential Manifolds

Author(s):

Ali S Rasheed, Faik Mayah and Ahmed A H AL-Jumaili

Ministry of Higher Education and Scientific Research,
Iraq.
E-mail: ahmedhashem@gmail.com
 

Department of Physics, College of Sciences,
University of Wasit,
Iraq.
E-mail: faik.mayah@gmail.com
 

Abstract:

In addition to solid ground of Riemannian manifolds fundamentals, this article interviews some popular optimization methods on Riemannian manifolds. Several optimization problems can be better stated on manifolds rather than Euclidean space, such as interior point methods, which in turns based on self-concordant functions (logarithmic barrier functions). Optimization schemes like the steepest descent scheme, the Newton scheme, and others can be extended to Riemannian manifolds. This paper introduces some Riemannian and non-Riemannian schemes on manifolds.

Paper's Title:

Semivectorial Bilevel Optimization on Affine-Finsler-Metric Manifolds

Author(s):

Faik Mayah¹, Ali S Rasheed² and Naseif J. Al- Jawari³

¹Department of Physics,
College of Sciences,
University of Wasit,
Iraq.
E-mail: faik.mayah@gmail.com

²Ministry of Higher Education and Scientific Research,
Iraq.
E-mail: ali.math2018@yahoo.com ahmedhashem@gmail.com

³Dept. of Mathematics,
College of Science,
Mustansiriyah University, Baghdad,
Iraq.
E-mail: nsaif642014@yahoo.com

Abstract:

A Finsler manifold is a differential manifold together with a Finsler metric, in this paper we construct a new class of Finsler metric affine manifolds on bilevel semivectorial with optimization problems. The first steps for this purpose involve the study of bilevel optimization on affine manifolds. The bilevel programming problem can be viewed as a static version of the noncooperative, two-person game which was introduced in the context of unbalanced economic markets. Bilevel optimization is a special kind of optimization where one problem is embedded within another.

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