If Z1 L p ([0, [), Z2 Lq ([0, [), 1 1 1 p, q, r 1 such that 1 p = 1, 1 q = 1 and 1 r = 1, then the following fractional integral p q r inequality holds: two|FI v1 h 1 F FI v1 h 1 Z1 Z2 – FI v1 h 1 Z1 FI v1 h 1 Z2 -FI v1 h 1 Z1 I v1 h 1 Z2 FI v1 h 1 FI v1 h 1 Z1 Z2 | Zr p1 pv1 qv(F – F) (F – F) FFh1h1 F – F F – F1 r| – | Zd dvr qv1 q(F – F) (F – F) FFh1h1 F – F F – F1 r| – |p Zpd dq vZ1 1 qv(F – F) (F – F) FFh1h1 F – F F – F| – |pd d .Remark 6. By thinking about h1 = h1 in Theorem four, we acquire Theorem three. Remark 7. If we contemplate = 1, F = and (F) = led towards the result of Dahmani [28].in Theorem four, then we areFractal Fract. 2021, five,13 of4. Concluding Remarks By using the proposed weighted-type generalized fractional integral operator, we established a class of new integral inequalities for differentiable functions connected to Chebyshev’s, weighted Chebyshev’s, and extended Chebyshev’s functionals. The obtained inequalities are in extra common kind than the existing inequalities, which happen to be published earlier in the literature. Our result’s exceptional circumstances might be located in [5,11,12,270]. Moreover, for other kinds of operators addressed in Remarks 1 and 2, specific new integral inequalities connected to Chebyshev’s functional and its extensions offered in the literature could be quickly obtained. One may possibly investigate particular other kinds of integral inequalities by employing the proposed operators inside the near future.Author Contributions: Conceptualization, G.R. and a.H.; methodology, G.R.; software, A.H.; validation, G.R., A.A. and K.S.N.; formal analysis, G.R., A.H. and K.S.N.; investigation, A.H.; sources, K.S.N. and R.N.M.; writing–original draft preparation, G.R., A.H. and K.S.N.; writing–review and editing, G.R., K.S.N. and R.N.M.; visualization, K.S.N.; supervision, G.R.; project administration, G.R. and K.S.N.; funding acquisition, R.N.M. All authors have study and agreed for the published version in the manuscript. Funding: This analysis received no external funding. Institutional Overview Board Statement: Not Applicable. Informed Consent Statement: Not Applicable. Information Availability Statement: Not Applicable. Acknowledgments: This work was supported by Taif Bay K 8644 Agonist University researchers supporting Project Number (TURSP-2020/102), Taif University, Taif, Saudi Arabia. Conflicts of Interest: The authors declare that they’ve no competing interest.galaxiesArticleBound on Photon Circular Orbits generally Relativity and BeyondSumanta ChakrabortySchool of Physical Sciences, Indian Association for the Cultivation of Science, Kolkata 700032, India; [email protected]: The existence of a photon circular orbit can inform us a good deal about the nature of your underlying spacetime, considering the fact that it plays a pivotal role inside the understanding of your characteristic signatures of compact objects, namely the quasi-normal modes and shadow radius. For this purpose, determination in the place of the photon circular orbit is of utmost value. Within this work, we derive bounds around the place of the photon circular orbit about compact objects within the Chetomin Formula purview of basic relativity and beyond. As we’ve got explicitly demonstrated, contrary towards the earlier benefits in the context of basic relativity, the bound on the location with the photon circular orbit is not necessarily an upper bound. Based on the matter content, it really is attainable to arrive at a decrease bound as well. This has intriguing implications for the quasi-normal modes and shadow radius, the two k.