Results 41 to 50 of about 291,483 (125)

The analytical solution of Van der Pol and Lienard differential equations within conformable fractional operator by retarded integral inequalities

Demonstratio Mathematica, 2019
In this study we introduced and tested retarded conformable fractional integral inequalities utilizing non-integer order derivatives and integrals. In line with this purpose, we used the Katugampola type conformable fractional calculus which has several ...
Usta Fuat, Sarıkaya Mehmet Zeki
doaj   +1 more source

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

Improved Hermite Hadamard type inequalities for harmonically convex functions via Katugampola fractional integrals

, 2019
In this paper,we proved three new Katugampola fractional Hermite- Hadamard type inequalities for harmonically convex functions by using the left and the right fractional integrals independently.
Kunt, Mehmet, Köroğlu, Tuncay, Şanlı, Zeynep   +2 more
core   +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

Fractal dimension of Katugampola fractional integral of vector-valued functions

, 2021
Calculating fractal dimension of the graph of a function not simple even for real-valued functions. While through this paper, our intention is to provide some initial theories for the dimension of the graphs of vector-valued functions.
Tanmoy Som, Saurabh Verma, Megha Pandey
core   +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

Computational Solution of Katugampola Conformable Fractional Differential Equations via RBF Collocation Method [PDF]

, 2017
2nd International Conference on Advances in Natural and Applied Sciences (ICANAS) -- APR 18-21, 2017 -- Antalya, TURKEYWOS: 000405093100046In conjunction with the development of fractional calculus, conformable derivatives and integrals has been widely ...
Fuat Usta, Usta, Fuat
core   +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