Results 51 to 60 of about 145 (127)

A Review of Certain Modern Special Functions and Their Applications

Abstract and Applied Analysis, Volume 2026, Issue 1, 2026.
This review article comprehensively analyzes recent developments in the generalization of special functions (SFs) and polynomials via various fractional calculus operators (FCOs), focusing on the analytical properties and applications of extended Hurwitz–Lerch zeta, Wright, and hypergeometric functions.
Hala Abd Elmageed, Mohamed Abdalla, AbdelMaksoud Soliman   +2 more
wiley   +1 more source

On the Solution Structure of Sequential φ‐Hilfer Fractional Differential Equations With p‐Laplacian Operator

Computational and Mathematical Methods, Volume 2026, Issue 1, 2026.
This work researches in a class of φ‐Hilfer FDEs with p‐Laplacian operator by evolving an appropriate analytical framework. We demonstrate the existence and uniqueness of solutions utilizing Banach′s fixed‐point theorem. Subsequently, an alternative theorem is applied to verify the existence of at least a single solution. In addition to the theoretical
Mohammed Kaid, Khellaf Ould Melha, Mohammad Esmael Samei, Sabri T. M. Thabet, Taoufik Moulahi, Thabet Abdeljawad, Higinio Ramos Calle   +6 more
wiley   +1 more source

Some inequalities obtained by fractional integrals of positive real orders

Journal of Inequalities and Applications, 2020
The primary objective of this study is to handle new generalized Hermite–Hadamard type inequalities with the help of the Katugampola fractional integral operator, which generalizes the Hadamard and Riemann–Liouville fractional integral operators into one
Mustafa Gürbüz, Yakup Taşdan, Erhan Set   +2 more
doaj   +1 more source

Some Solutions of Hilfer Fractional Volterra Integral Equations by Using Pathway‐Type Transform

International Journal of Mathematics and Mathematical Sciences, Volume 2026, Issue 1, 2026.
The Pathway‐type Pε‐transform technique has been introduced as a versatile binomial transform encompassing various classes, including the classical Laplace transform. In this paper, we apply this technique to derive solutions for fractional Volterra integral equations (FVIEs) and fractional Abel–Volterra integral equations (FAVIEs) that involve Hilfer ...
Faten H. Damag, Mohammad Alshammari, Amin Saif, Mohammed S. Alsharafi, Adem Kilicman, Shikha Binwal   +5 more
wiley   +1 more source

Generalized Composite Fractional Derivatives and Integral Operators With Incomplete R‐Function Kernels

International Journal of Mathematics and Mathematical Sciences, Volume 2026, Issue 1, 2026.
Fractional differential equations (FDEs) have received a lot of interest because of their diverse applications in engineering, mathematical physics, chemistry, and biology. This study introduces a new family of fractional integral operators using incomplete R‐function kernels, advancing the theoretical foundation of FDEs further.
Priti Purohit, Ravi Gupta, Shyamsunder, Biniyam Shimelis, Shikha Binwal   +4 more
wiley   +1 more source

Comparison of Integer‐, Constant‐, and Variable‐Order Fractional Models of Competition for Student Population Using Caputo–Fabrizio Fractional Derivative With Policy Interventions

International Journal of Mathematics and Mathematical Sciences, Volume 2026, Issue 1, 2026.
This study develops constant‐order (CO) and variable‐order (VO) Caputo–Fabrizio (CF) fractional derivative (CFFD) models to extend the classical integer‐order framework for analyzing competition among public, private, and nonenrolled student populations under varying policy intervention intensities.
Kiprotich Ezra Bett, Cyrus Gitonga Ngari, Grace Gakii Muthuri, Kareem Elgindy   +3 more
wiley   +1 more source

Ostrowski-type fractional integral inequalities for mappings whose derivatives are h-convex via Katugampola fractional integrals [PDF]

Studia Universitatis Babes-Bolyai Matematica, 2018
In this paper we generalize some Riemann-Liouville fractional integral inequalities of Ostrowski type for h-convex functions via Katugampola fractional integrals, generalization of Riemann- Liouville and the Hadamard fractional integrals. Also we deduce some known results by using p-functions, convex functions and s-convex functions.
Ghulam Farid, Udita N. Katugampola, Muhammad Usman   +2 more
openaire   +1 more source

Error Bound of Hermite–Hadamard–Mercer Inequalities via ψ−Conformable Fractional Integral Operators on the Coordinates

International Journal of Mathematics and Mathematical Sciences, Volume 2026, Issue 1, 2026.
This paper develops a family of Hermite–Hadamard–Mercer‐type inequalities within the framework of generalized conformable fractional calculus. By interpreting generalized conformable fractional integrals as weighted integral means depending on the order parameter, we derive refined two‐sided bounds for coordinated convex functions that incorporate ...
Jen Chieh Lo, Mohammad Rezwan Habib
wiley   +1 more source

Estimates of upper bound for differentiable mappings related to Katugampola fractional integrals and $ p $-convex mappings

AIMS Mathematics, 2021
We use the definition of a fractional integral operators, recently introduced by Katugampola, to establish a parameterized identity associated with differentiable mappings. The identity is then used to derive the estimates of upper bound for mappings whose first derivatives absolute values are p-convex mappings.
Yuping Yu, Hui Lei, Gou Hu, Tingsong Du
openaire   +2 more sources

Solution of Time‐Fractional Coupled Burgers Equations by the Yang Transform Adomian Decomposition Method

Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.
In this paper, the Yang transform Adomian decomposition method (YTADM) is employed in the solution of nonlinear time‐fractional coupled Burgers equations. The technique solves the fractional and nonlinear terms successfully via the Adomian decomposition of the Yang transform.
Mustafa Ahmed Ali, Mehmet Merdan, Yeou Jiann Lim   +2 more
wiley   +1 more source