Results 41 to 50 of about 582,662 (170)
New Fractional Integral Inequalities for Convex Functions Pertaining to Caputo–Fabrizio Operator
Fractal and Fractional, 2022 In this article, a generalized midpoint-type Hermite–Hadamard inequality and Pachpatte-type inequality via a new fractional integral operator associated with the Caputo–Fabrizio derivative are presented.
Soubhagya Kumar Sahoo +4 more
doaj +1 more source
Asian Journal of Control, Volume 28, Issue 1, Page 34-45, January 2026.Abstract We study a nonlinear ψ−$$ \psi - $$ Hilfer fractional‐order delay integro‐differential equation ( ψ−$$ \psi - $$ Hilfer FrODIDE) that incorporates N−$$ N- $$ multiple variable time delays. Utilizing the ψ−$$ \psi - $$ Hilfer fractional derivative ( ψ−$$ \psi - $$ Hilfer‐FrD), we investigate the Ulam–Hyers––Rassias (U–H–R), semi‐Ulam–Hyers ...
Cemil Tunç, Osman Tunç
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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 +2 more
wiley +1 more source
Journal of Function Spaces, 2021 We investigate a nonlinear system of pantograph-type fractional differential equations (FDEs) via Caputo-Hadamard derivative (CHD). We establish the conditions for existence theory and Ulam-Hyers-type stability for the underlying boundary value system ...
Zareen A. Khan, Israr Ahmad, Kamal Shah
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Advances in Mathematical Physics, Volume 2026, Issue 1, 2026.Fractional calculus (FC) has become more popular during the past four decades due to its extensive applications in mathematics, physics, engineering, and statistics. B‐spline functions offer flexible and incredibly precise approximations because of their piecewise polynomial structure and smoothness at knots.
Syeda Alishba Batool +5 more
wiley +1 more source
Dynamics of the Caputo fractional derivative [PDF]
In this article we analyse the dynamical behaviour of the Caputo complex fractional derivative. We prove that the Caputo complex fractional derivative operator is Devaney chaotic in the Mittag-Leffler Caputo space.
Murillo-Arcila, Marina +5 more
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Numerical methods for fractional differential equations by new caputo and hadamard types operators [PDF]
, 2020 Fractional ordinary differential equation (FODE) and fractional partial differential equation (FPDE) emerges in various modelling of physics phenomena. Over past decades, several fractional derivative and operator has been introduced such as Caputo-
Toh, Yoke Teng
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Electronic Journal of Differential Equations, 2016 Firstly we prove existence and uniqueness of solutions of Cauchy problems of linear fractional differential equations (LFDEs) with two variable coefficients involving Caputo fractional derivative, Riemann-Liouville derivative, Caputo type Hadamard ...
Yuji Liu
doaj
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 +6 more
wiley +1 more source
Fractal and Fractional, 2021 In this work, we explore the existence results for the hybrid Caputo–Hadamard fractional boundary value problem (CH-FBVP). The inclusion version of the proposed BVP with a three-point hybrid Caputo–Hadamard terminal conditions is also considered and the ...
Muhammad Yaseen +3 more
doaj +1 more source