Muhammad Shoaib Saleem

Bio: Muhammad Shoaib Saleem is an academic researcher from University of Okara. The author has contributed to research in topics: Convex function & Hermite polynomials. The author has an hindex of 6, co-authored 46 publications receiving 195 citations. Previous affiliations of Muhammad Shoaib Saleem include University of Education.

Bounds of Riemann-Liouville Fractional Integrals in General Form via Convex Functions and Their Applications

Abstract: In this article, we establish bounds of sum of the left and right sided Riemann Liouville (RL) fractional integrals and related inequalities in general form. A new and novel approach is followed to obtain these results for general Riemann Liouville (RL) fractional integrals. Monotonicity and convexity of functions are used with some usual and straight forward inequalities. The presented results are also have connection with some known and already published results. Applications and motivations of presented results are briefly discussed.

Elliptic function solutions, modulation instability and optical solitons analysis of the paraxial wave dynamical model with Kerr media

Abstract: The optical solitary waves explain non-dispersive and non-diffractive spatiotemporal localized waves envelopes promulgating in the media of optical Kerr. These propagations are generally described by the nonlinear Schro dinger equation. The modified extended mapping technique is utilized to assemble the solitons, solitary waves and rational solutions of time-dependent dimensionless paraxial wave equation. The obtained different sorts of wave solutions encompass key applications in physics and engineering. By giving appropriate values to parameter, special sorts of solitary waves configuration can be displayed graphically. The physical interpretation of the solution can be understood through the structure. The stability of this wave equation is investigated via using modulational instability analysis which authenticates that all soliton solutions are stable and exact. Several analytical results and working out have confirmed the strength and efficacy of the current technique.

I and i

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

Theory Of Vector Optimization

Abstract: Well, someone can decide by themselves what they want to do and need to do but sometimes, that kind of person will need some theory of vector optimization references. People with open minded will always try to seek for the new things and information from many sources. On the contrary, people with closed mind will always think that they can do it by their principals. So, what kind of person are you?