Results 81 to 90 of about 13,452 (220)

Mellin Transforms of the Generalized Fractional Integrals and Derivatives

, 2014
We obtain the Mellin transforms of the generalized fractional integrals and derivatives that generalize the Riemann-Liouville and the Hadamard fractional integrals and derivatives.
Bucchianico, Butkovskii, Butzer, Butzer, Butzer, Butzer, Bóna, Erdélyi, Erdélyi, Flajolet, Gaboury, Goldman, Hadamard, Herrmann, Katugampola, Katugampola, Kilbas, Kilbas, Kilbas, Kilbas, Kiryakova, Machado, Miller, Noor, Noor, Noor, Odzijewicz, Odzijewicz, Odzijewicz, Oldham, Podlubny, Pooseh, Robbins, Robinson, Rodrigues, Roman, Roman, Roman, Rota, Rota, Samko, Udita N. Katugampola, Yakubovich   +42 more
core   +1 more source

Analytical Study of Variable‐Order Fractional Differential Equations With Initial and Terminal Antiperiodic Boundary Conditions

Journal of Applied Mathematics, Volume 2025, Issue 1, 2025.
This study investigates the existence, uniqueness, and stability of solutions to Riemann–Liouville fractional differential equations with fractional variable‐order and antiperiodic boundary conditions. By employing the Banach fixed point theorem, we establish conditions for the uniqueness of solutions, while Schauder’s fixed point theorem is used to ...
Mohammed Said Souid, Zoubida Bouazza, M’hamed Bensaid, K. Sudar Mozhi, Mokhtari Mokhtar, Joshua Kiddy K. Asamoah, Mohammad Rezwan Habib   +6 more
wiley   +1 more source

Estimations of the Disparity Between Hydrogen Ion Concentration and pH in the Context of Caputo–Fabrizio Fractional Integrals via Convexity

Journal of Function Spaces, Volume 2025, Issue 1, 2025.
Fractional calculus is unique due to the fact it is as old as regular (integer) calculus, but it has also expanded its applications in a variety of fields and on a diversity of topics over the course of the last century. This leads to a continuous increase in the number of researchers and papers, ranging from integral inequality to biological models ...
Maria Tariq, Ammara Nosheen, Khuram Ali Khan, Atiq Ur Rehman, Ndolane Sene, Nikhil Khanna   +5 more
wiley   +1 more source

Recovering the space source term for the fractional-diffusion equation with Caputo–Fabrizio derivative

Journal of Inequalities and Applications, 2021
This article is devoted to the study of the source function for the Caputo–Fabrizio time fractional diffusion equation. This new definition of the fractional derivative has no singularity. In other words, the new derivative has a smooth kernel.
Le Nhat Huynh, Nguyen Hoang Luc, Dumitru Baleanu, Le Dinh Long   +3 more
doaj   +1 more source

A New Double Transform for Nonconformable Derivatives

Journal of Function Spaces, Volume 2025, Issue 1, 2025.
In this article, we present the nonconformable fractional derivative of the double Sumudu transformation. In this study, we investigate the main features and benefits of this new technique and then apply it to solve several fractional nonconformable partial differential equations.
Shams A. Ahmed, Tarig M. Elzaki, Nikhil Khanna   +2 more
wiley   +1 more source

The general solution of differential equations with Caputo-Hadamard fractional derivatives and impulsive effect [PDF]

Advances in Difference Equations, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +1 more source

Advanced Fixed Point Methods for Analyzing Coupled Caputo Q‐Fractional Boundary Value Problems With Supportive Examples

Journal of Function Spaces, Volume 2025, Issue 1, 2025.
This article analyzes a complex coupled system of multipoint nonlinear boundary value problems involving Caputo‐type fractional discrete differential equations with multiple fractional q−integrals. We establish the uniqueness and existence of solutions using a rigorous approach grounded in fixed‐point theory, specifically Banach’s fixed‐point theorem ...
Hasanen A. Hammad, Saleh Fahad Aljurbua, Asamh Saleh M. Al Luhayb, Baowei Feng   +3 more
wiley   +1 more source

Practical Stability of Observer-Based Control for Nonlinear Caputo–Hadamard Fractional-Order Systems

Fractal and Fractional
This paper investigates the problem of observer-based control for a class of nonlinear systems described by the Caputo–Hadamard fractional-order derivative.
Rihab Issaoui, O. Naifar, M. Tlija, Lassaad Mchiri, A. Ben Makhlouf   +4 more
semanticscholar   +1 more source

New Fractional Hermite–Hadamard-Type Inequalities for Caputo Derivative and MET-(p, s)-Convex Functions with Applications

Fractal and Fractional
This article investigates fractional Hermite–Hadamard integral inequalities through the framework of Caputo fractional derivatives and MET-(p,s)-convex functions.
Muhammad Sajid Zahoor, Amjad Hussain, Yuanheng Wang   +2 more
doaj   +1 more source

On Cauchy problems with Caputo Hadamard fractional derivatives

, 2016
Summary: The current work is motivated by the so-called Caputo-type modification of the Hadamard or Caputo Hadamard fractional derivative. The main aim of this paper is to study Cauchy problems for a differential equation with a left Caputo Hadamard fractional derivative in spaces of continuously differentiable functions.
Adjabi, Y., Jarad, Fahd, Baleanu, D., Abdeljawad, T.   +3 more
openaire   +2 more sources