Results 131 to 140 of about 1,565,786 (254)

Generalized Sumudu transform and tempered ξ-Caputo fractional derivative

Filomat
This paper applied the generalized Sumudu transform to the tempered ?-Hilfer fractional integral and the tempered ?-Caputo fractional derivative. Our findings are utilized to address non homo-geneous linear fractional differential equations in an initial value problem involving the tempered ?-Caputo fractional derivative of an order ?
Khadija Elkhalloufy, Khalid Hilal, Ahmed Kajouni   +2 more
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Bernstein Operational Matrix for Solving Variable Order Fractional Differential Equations with Generalized Caputo-Type

Wasit Journal for Pure Sciences
In this research, we present novel generalized derivative founded on the newly constructed (NGCFVODs) novel generalized Caputo  Fractional variable order derivatives.
alaa abbas
doaj   +1 more source

EXISTENCE RESULTS FOR A NONLINEAR GENERALIZED CAPUTO FRACTIONAL BOUNDARY VALUE PROBLEM

Journal of Applied Analysis & Computation
The paper investigates the existence of solutions for a three-point boundary value problem involving a generalized Caputo fractional derivative. Fractional calculus is widely used to model complex phenomena with memory effects and anomalous diffusion.
Yalçın S., Çetin E., Topal F.S.
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Caputo gH-differentiability for Gronwalls inequality: insight, new results and application

Journal of Inequalities and Applications
This paper investigates Gronwall’s inequality within the framework of interval-valued functions under Caputo gH-differentiability. Employing interval-valued Caputo fractional derivatives and associated interval-valued Riemann–Liouville integrals, we ...
Fatima Khan, Anum Zehra, Muhammad Farman, Kottakkaran Sooppy Nisar, Aceng Sambas, Mohamed Hafez   +5 more
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Estimates related to Caputo derivatives using generalized modified $ h $-convex functions

AIMS Mathematics
<p>In the present work, we have established some new fractional integral inequalities for functions whose $ k $th-derivatives are generalized modified $ h $-convex and symmetric about the midpoint involving the Caputo fractional derivatives. Many particular cases are obtained by using the findings.</p>
Halim Benali, Mohammed Said Souid, Hatıra Günerhan, Unai Fernandez-Gamiz   +3 more
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Conformable and Caputo’s Derivatives in Generalized Viscoelastic Models

Applied Mathematics, 2023
Jorge Fujioka, Rosalío Fernando Rodríguez, Áurea Espinosa-Cerón   +2 more
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Generalized solutions of the Cauchy problem involving $\Phi$-Caputo fractional derivatives

Boletim da Sociedade Paranaense de Matemática
The main objective of this research paper is to embed $\Phi$-Caputo fractional derivative in the Colombeau algebra of generalized functions and we investigate the existence and uniqueness of the Cauchy problem involving $\Phi$-Caputo fractional derivatives in the extended Colombeau algebras.
Abdellah Taqbibt, Latifa El Bezdaoui, M'hamed Elomari, Lalla Saâdia Chadli   +3 more
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A General Framework for the Multiplicity of Positive Solutions to Higher-Order Caputo and Hadamard Fractional Functional Differential Coupled Laplacian Systems

Fractal and Fractional
This paper applies a general framework to explore the existence of multiple positive solutions for the fractional integral boundary value problem of high-order Caputo and Hadamard fractional coupled Laplacian systems with delayed or advanced arguments ...
Kaihong Zhao, Xiaoxia Zhao, Xiaojun Lv
doaj   +1 more source

A new scheme for the solution of the nonlinear Caputo–Hadamard fractional differential equations

Alexandria Engineering Journal
This paper introduces a numerical approach by generalizing Legendre wavelets for solving nonlinear Caputo–Hadamard fractional differential equations. The methodology involves the extension of classical Legendre wavelets, namely the generalized Legendre ...
Umer Saeed, Mujeeb ur Rehman
doaj   +1 more source

Generalized cauchy problem: caputo type

, 2009
Fractional derivatives, or more precisely derivatives of arbitrary orders, have played a significant role in engineering, sciences, pure and applied mathematics in recent years. Several types of fractional derivative and integral have proposed. These definitions include Riemann-Liouville fractional derivative and integral.
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