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A comprehensive review of the Pachpatte-type inequality pertaining to fractional integral operators [PDF]

Surveys in Mathematics and its Applications
In the frame of fractional calculus, the term convexity is primarily utilized to address several challenges in both pure and applied research. The main focus and objective of this review paper is to present Pachpatte-type inequalities involving a variety
Muhammad Tariq, Asif Ali Shaikh, Sotiris K. Ntouyas   +2 more
doaj  

Riemann–Liouville Type Fractional Derivatives and Equivalences of Linear Riemann–Liouville Type Fractional Differential Equations

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT The first or higher order Riemann–Liouville (R‐L) type fractional derivatives are studied. The relations between the R‐L type fractional derivatives and the classical R‐L fractional derivatives are obtained and the spaces of functions on which the R‐L type fractional derivatives exist are provided.
Kunquan Lan
wiley   +1 more source

Sliding Mode Control in Aerospace Applications: A Survey

International Journal of Robust and Nonlinear Control, EarlyView.
ABSTRACT Sliding mode control (SMC) enjoys robustness to matched and unmatched (in the case of minimum phase input‐output dynamics) bounded perturbations, and finite time convergence. Second‐order and higher‐order sliding mode control systems (2‐SMC/HOSMC) retain all the advantages of sliding mode control, but in addition can be applied to systems of ...
Yuri Shtessel, Christopher Edwards
wiley   +1 more source

Fractional Integral Inequalities of Riemann–Liouville Type for Higher‐Order Differentiable Convex Mappings

Mathematical Methods in the Applied Sciences, Volume 49, Issue 11, Page 12313-12323, 30 July 2026.
ABSTRACT In this paper, we investigate several Riemann–Liouville fractional integral inequalities for higher‐order differentiable functions using a simple and novel approach. First, we present an inequality involving fractional integrals that generalizes the right‐hand side of the fundamental Hermite–Hadamard inequality to higher‐order derivatives ...
Samet Erden, Hüseyin Budak
wiley   +1 more source

On Fractional Hermite–Hadamard-Type Inequalities for Harmonically s-Convex Stochastic Processes

Fractal and Fractional
In this paper, we investigate Hermite–Hadamard-type inequalities for harmonically s-convex stochastic processes via Riemann–Liouville fractional integrals. We begin by introducing the notion of harmonically s-convex stochastic processes. Subsequently, we
Rabab Alzahrani, Raouf Fakhfakh, Ghadah Alomani, Badreddine Meftah   +3 more
doaj   +1 more source

Some New Generalizations for Exponentially s-Convex Functions and Inequalities via Fractional Operators

Fractal and Fractional, 2019
The main objective of this paper is to obtain the Hermite−Hadamard-type inequalities for exponentially s-convex functions via the Katugampola fractional integral.
Saima Rashid, Muhammad Aslam Noor, Khalida Inayat Noor, Ahmet Ocak Akdemir   +3 more
doaj   +1 more source

Finite Biorthogonal Polynomials Suggested by the Finite Orthogonal Polynomials Mnp,qx$$ {M}_n^{\left(p,q\right)}(x) $$

Mathematical Methods in the Applied Sciences, Volume 49, Issue 11, Page 12524-12538, 30 July 2026.
ABSTRACT Constructing a biorthogonal structure from scratch, that is, defining a biorthogonal pair is quite tough. Because here the orthogonality must be established between two different sets. There are four known univariate biorthogonal polynomial sets, suggested by Laguerre, Jacobi, Hermite and Szegő‐Hermite polynomials, in the literature.
Esra Güldoğan Lekesiz
wiley   +1 more source

Wirtinger-type inequalities for Caputo fractional derivatives via Taylor’s formula

Journal of Inequalities and Applications
In this study, we firstly derive a Wirtinger-type result, which gives the connection in between the integral of square of a function and the integral of square of its Caputo fractional derivatives with the help of left-sided and right-sided fractional ...
Samet Erden, Mehmet Zeki Sarıkaya, Burçin Gokkurt Ozdemir, Neslihan Uyanık   +3 more
doaj   +1 more source

On some integral inequalities for (k,h)-Riemann-Liouville fractional integral

New Trends in Mathematical Science, 2016
In this study, giving the definition of fractional integral, which are with the help of synchronous and monotonic function, some fractional integral inequalities have established.
AKKURT, Abdullah, YİLDİRİM, M. Esra, YİLDİRİM, Huseyin Yildirim   +2 more
openaire   +2 more sources

New Approach to Weighted Newton‐Type Inequalities Using Riemann–Liouville Fractional Integrals

Mathematical Methods in the Applied Sciences, Volume 49, Issue 10, Page 11186-11204, 15 July 2026.
ABSTRACT In this investigation paper, we present some weighted inequalities Newton‐type for various classes of functions utilizing Riemann–Liouville fractional integrals. The study begins by introducing a positive weighted function to derive a key integral equality essential for proving the main results.
Rubayyi T. Alqahtani, Hüseyin Budak
wiley   +1 more source