Results 51 to 60 of about 408 (175)

Approximate Analytical Solutions of the Time‐Fractional Swift–Hohenberg Equation via Yang Transform Adomian Decomposition Method

Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.
This study examines approximate analytical solutions of the time‐fractional Swift–Hohenberg equation involving the Caputo–Fabrizio fractional derivative. The main objective of this study is to investigate efficient analytical approximation techniques using the Yang transform Adomian decomposition method (YTADM).
Mustafa Ahmed Ali, Mehmet Merdan, Serbay Duran   +2 more
wiley   +1 more source

Existence and Attractivity of Mild Solutions for Fractional Diffusion Equations Involving the Regularized ψ-Hilfer Fractional Derivatives

Axioms
The regularized ψ-Hilfer derivative within the sense of Caputo is an improved version of the ψ-Hilfer fractional derivative, primarily because it addresses the issue where the initial conditions of problems involving the ψ-Hilfer fractional derivative ...
Luyao Wang, Yuhang Jin, Wenchang He, Jia Mu   +3 more
doaj   +1 more source

Exact and Approximate Controllability for Backward Fractional Integro‐Differential Equations With History‐Dependent Operators

Journal of Function Spaces, Volume 2026, Issue 1, 2026.
This paper is devoted to the analysis of controllability for a class of backward fractional integro‐differential equations involving history‐dependent operators, which arise naturally in systems with memory effects. The study begins with the formulation of an appropriate functional framework, within which the concept of approximate controllability is ...
Ghadah Albeladi, Hasanen A. Hammad, Baowei Feng   +2 more
wiley   +1 more source

Study of a boundary value problem for fractional order $$\psi $$-Hilfer fractional derivative [PDF]

Arabian Journal of Mathematics, 2019
Abstract This manuscript is devoted to the existence theory of a class of random fractional differential equations (RFDEs) involving boundary condition (BCs). Here we take the corresponding derivative of arbitrary order in $$\psi $$ ψ -Hilfer sense. By utilizing classical fixed point theory and nonlinear analysis we establish some basic results of the ...
S. Harikrishnan, Kamal Shah, K. Kanagarajan   +2 more
openaire   +1 more source

On the Stability of Fractional Integro‐Differential Equations of Ψ‐Hilfer Type

Journal of Function Spaces, Volume 2026, Issue 1, 2026.
In this article, we investigate some properties such as the existence, uniqueness, and Ulam–Hyers–Rassias stability for the fractional Volterra–Fredholm integrodifferential equations of Ψ‐Hilfer type with boundary conditions. We prove the desired results by using the Banach fixed point theorem and the Schauder fixed point theorem.
Malayin A. Mohammed, Sahar M. A. Maqbol, Ram G. Metkar, Udhayakumar Ramalingam   +3 more
wiley   +1 more source

Leibniz type rule: $Ψ-$Hilfer fractional derivative

, 2018
In this paper, we present the Leibniz rule for the $Ψ-$Hilfer ($Ψ-$H) fractional derivative in two versions, the first in relation to $Ψ-$RL fractional derivative and the second in relation to the $Ψ-$H fractional derivative. In this sense, we present some particular cases of Leibniz rules and Leibniz type rules from the investigated case.
Sousa, J. Vanterler da C., de Oliveira, E. Capelas   +1 more
openaire   +2 more sources

From fractional differential equations with Hilfer derivatives

Computational and Applied Mathematics, 2021
In this article, we proposed new discrete maps with memory (DMM). These maps are derived from fractional differential equations (FDE) with the Hilfer fractional derivatives of non-integer orders and periodic sequence of kicks. The suggested DMM are obtained from these equations without any approximation, and they are a discrete form of the exact ...
openaire   +2 more sources

A numerical approach for multi-dimensional ψ-Hilfer fractional nonlinear Galilei invariant advection–diffusion equations

Results in Physics
In this paper, we introduce the ψ-Hilfer fractional version of nonlinear Galilei-invariant advection–diffusion equations in one and two dimensions. A new type of basic functions, namely the ψ-Chebyshev cardinal functions (CFs), is introduced to establish
M.H. Heydari, M. Razzaghi, M. Bayram
doaj   +1 more source

A comprehensive review of the Hermite-Hadamard inequality pertaining to fractional differential operators [PDF]

Surveys in Mathematics and its Applications, 2023
A review on Hermite-Hadamard type inequalities connected with a different classes of convexities and fractional differential operators is presented. In the various classes of convexities it includes, classical convex functions, quasi-convex functions, p ...
Muhammad Tariq, Sotiris K. Ntouyas, Asif Ali Shaikh, Jessada Tariboon   +3 more
doaj  

Resolvents Operators Approach to Mild Solutions for Caputo Fractional Functional Differential Equations

Journal of Mathematics, Volume 2026, Issue 1, 2026.
This study examines a fractional functional differential equation using the Caputo derivative. Its main goal is to introduce the resolvent operator to define the analytical solution, and then use it to show the existence of a mild solution. An illustrative example will highlight the primary result.
Ndolane Sene, Karima Abdelmalek, Smritijit Sen   +2 more
wiley   +1 more source