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  1. Article

    Open Access

    More properties of the proportional fractional integrals and derivatives of a function with respect to another function

    In this article, we present some new properties of the fractional proportional derivatives of a function with respect to a certain function. We use a modified Laplace transform to find the relation between the...

    Fahd Jarad, Thabet Abdeljawad, Saima Rashid in Advances in Difference Equations (2020)

  2. No Access

    Article

    A New \((3+1)\) -dimensional Hirota Bilinear Equation: Its Bäcklund Transformation and Rational-type Solutions

    The behavior of specific dispersive waves in a new \((3+1)\) -dimensional Hirota bilinear (3D-HB) equation is studied. A Bäcklun...

    Kamyar Hosseini, Majid Samavat, Mohammad Mirzazadeh in Regular and Chaotic Dynamics (2020)

  3. Article

    Open Access

    New quantum estimates in the setting of fractional calculus theory

    In this article, the investigation is centered around the quantum estimates by utilizing quantum Hahn integral operator via the quantum shift operator ψ q η ( ζ ) = q ζ + ( 1 − q ) η ${}_{\eta}\psi_{\math...

    Saima Rashid, Zakia Hammouch, Rehana Ashraf in Advances in Difference Equations (2020)

  4. Article

    Open Access

    Some new local fractional inequalities associated with generalized \((s,m)\) -convex functions and applications

    Fractal analysis is one of interesting research areas of computer science and engineering, which depicts a precise description of phenomena in modeling. Visual beauty and self-similarity has made it an attract...

    Thabet Abdeljawad, Saima Rashid, Zakia Hammouch in Advances in Difference Equations (2020)

  5. Article

    Open Access

    Certain new weighted estimates proposing generalized proportional fractional operator in another sense

    The present work investigates the applicability and effectiveness of generalized proportional fractional integral ( GPFI \(\mathcal{GPFI}\) ) operator in another sense. We aim to derive novel weighted generalizat...

    Thabet Abdeljawad, Saima Rashid, A. A. El-Deeb in Advances in Difference Equations (2020)

  6. Article

    Open Access

    Some new Simpson-type inequalities for generalized p-convex function on fractal sets with applications

    The present article addresses the concept of p-convex functions on fractal sets. We are able to prove a novel auxiliary result. In the application aspect, the fidelity of the local fractional is used to establish...

    Thabet Abdeljawad, Saima Rashid, Zakia Hammouch in Advances in Difference Equations (2020)

  7. Article

    Open Access

    New fractional approaches for n-polynomial P-convexity with applications in special function theory

    Inequality theory provides a significant mechanism for managing symmetrical aspects in real-life circumstances. The renowned distinguishing feature of integral inequalities and fractional calculus has a solid ...

    Shu-Bo Chen, Saima Rashid, Muhammad Aslam Noor in Advances in Difference Equations (2020)

  8. Article

    Open Access

    Integral inequalities via Raina’s fractional integrals operator with respect to a monotone function

    We establish certain new fractional integral inequalities involving the Raina function for monotonicity of functions that are used with some traditional and forthright inequalities. Taking into consideration t...

    Shu-Bo Chen, Saima Rashid, Zakia Hammouch in Advances in Difference Equations (2020)

  9. Article

    Analysis and dynamics of a mathematical model to predict unreported cases of COVID-19 epidemic in Morocco

    In December 2019, in Wuhan, China, a new disease was detected, and the virus easily spread throughout other nations. March 2, 2020, Morocco announced 1st infection of coronavirus. Morocco verified a total of 6...

    Abdelouahed Alla Hamou, Rando R. Q. Rasul in Computational and Applied Mathematics (2022)

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