Results 91 to 100 of about 582,712 (204)

On Extended Caputo Fractional Derivative Operator

, 2017
The main objective of this present paper is to introduce further extension of extended Caputo fractional derivative operator and establish the extension of an extended fractional derivative of some known elementary functions.
Gauhar Rahman, Muhammad Arshad, Kottakkaran Sooppy Nisar   +2 more
core   +1 more source

Existence and Stability Theorems for Implicit Neutral Fractional Integrodifferential Equations With Computational Results

Journal of Function Spaces, Volume 2026, Issue 1, 2026.
This paper investigates a class of nonlinear implicit neutral integrodifferential equations involving Hilfer–Katugampola fractional operators, which provide an effective framework for describing dynamical systems with memory and hereditary properties. By converting the considered problem into an equivalent fractional integral equation, we show that the
Manal Elzain Mohamed Abdalla, Hasanen A. Hammad, Tarek Aboelenen, Mohammed S. Abdo   +3 more
wiley   +1 more source

A Boundary Value Problem with Caputo–Hadamard Fractional Derivative: Analysis and Numerical Solution

European Journal of Pure and Applied Mathematics
We investigate a boundary-value problem governed by a fractional differential equation, which is non-linear. The fractional derivative is the combined Caputo-Hadamard fractional derivative. We establish the required conditions for the existence and uniqueness of solutions utilising the two standard fixed-point theorems, Banach fixed-point and Sadovskii
Afrah Hasan, Shayma Murad
openaire   +1 more source

A numerical framework based on piecewise Chebyshev cardinal functions for fractional integro-differential equations

Results in Applied Mathematics
In this study, we develop an operational matrix technique to address a set of fractional nonlinear integro-differential equations with the Caputo–Hadamard derivative. We utilize a family of the piecewise Chebyshev cardinal functions as basis functions in
S. Mansoori Aref, M.H. Heydari, M. Bayram   +2 more
doaj   +1 more source

Fractional Integral Inequalities via Caputo k‐Derivatives for Generalized Strongly Modified h‐Convex Functions

Journal of Function Spaces, Volume 2026, Issue 1, 2026.
This paper is devoted to the investigation of new fractional integral (FI) inequalities involving Caputo k‐fractional derivatives (CKFDs) for functions whose higher order derivatives satisfy the generalized strongly modified h‐convexity (GSMHC) condition. By combining the analytical properties of generalized convexity with the framework of k‐fractional
Mohammed Said Souid, Halim Benali, Sabri T. M. Thabet, Taoufik Moulahi, Al-Taweel Ahmed   +4 more
wiley   +1 more source

Incomplete Caputo fractional derivative operators

, 2018
The main aim of this paper is to give the definitions of Caputo fractional derivative operators and show their use in the special function theory. For this purpose, we introduce new types of incomplete hypergeometric functions and obtain their integral ...
Mehmet Ali Özarslan, Ceren Ustaoglu
core   +1 more source

Caputo-type modification of the Hadamard fractional derivatives [PDF]

, 2012
Generalization of fractional differential operators was subjected to an intense debate in the last few years in order to contribute to a deep understanding of the behavior of complex systems with memory effect. In this article, a Caputo-type modification
Thabet Abdeljawad, Abdeljawad, Thabet, Baleanu, Dumitru, Dumitru Baleanu, Jarad, Fahd, Fahd Jarad   +5 more
core   +1 more source

On Some Impulsive Fractional Integro-Differential Equation with Anti-Periodic Conditions

Fractal and Fractional
We investigate a class of boundary value problems (BVPs) involving an impulsive fractional integro-differential equation (IF-IDE) with the Caputo–Hadamard fractional derivative (C-HFD). We employ some fixed-point theorems (FPTs) to study the existence of
Ymnah Alruwaily, Kuppusamy Venkatachalam, El-sayed El-hady   +2 more
doaj   +1 more source

Spectral approximations to the fractional integral and derivative [PDF]

, 2012
In this paper, the spectral approximations are used to compute the fractional integral and the Caputo derivative. The effective recursive formulae based on the Legendre, Chebyshev and Jacobi polynomials are developed to approximate the fractional ...
Li, Changpin, Liu, Fawang, Fanhai Zeng, Changpin Li, Zeng, Fanhai, Fawang Liu   +5 more
core   +2 more sources

On Averaging Principle for Caputo–Hadamard Fractional Stochastic Differential Pantograph Equation

, 2022
In this paper, we studied an averaging principle for Caputo–Hadamard fractional stochastic differential pantograph equation (FSDPEs) driven by Brownian motion.
Mounia Mouy, Yamina Laskri, Hamid Boulares, Saleh Alshammari, Mohammad Alshammari, Wael W. Mohammed   +5 more
core   +1 more source