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18 Results Found

  • Review
  • Open Access
93 Citations
4,902 Views
22 Pages

2 December 2021

Often referred to as special functions or mathematical functions, the origin of many members of the remarkably vast family of higher transcendental functions can be traced back to such widespread areas as (for example) mathematical physics, analytic...

  • Article
  • Open Access
40 Citations
3,582 Views
19 Pages

In this research, we present a new computational technique for solving some physics problems involving fractional-order differential equations including the famous Bagley–Torvik method. The model is considered one of the important models to sim...

  • Article
  • Open Access
2 Citations
1,493 Views
14 Pages

Post-Pandemic Sector-Based Investment Model Using Generalized Liouville–Caputo Type

  • Muath Awadalla,
  • Muthaiah Subramanian,
  • Prakash Madheshwaran and
  • Kinda Abuasbeh

24 March 2023

In this article, Euler’s technique was employed to solve the novel post-pandemic sector-based investment mathematical model. The solution was established within the framework of the new generalized Caputo-type fractional derivative for the syst...

  • Article
  • Open Access
15 Citations
2,395 Views
17 Pages

Fractional Evolution Equations with Infinite Time Delay in Abstract Phase Space

  • Ahmed Salem,
  • Kholoud N. Alharbi and
  • Hashim M. Alshehri

17 April 2022

In the presented research, the uniqueness and existence of a mild solution for a fractional system of semilinear evolution equations with infinite delay and an infinitesimal generator operator are demonstrated. The generalized Liouville–Caputo...

  • Article
  • Open Access
12 Citations
1,750 Views
15 Pages

In this article, the authors propose to investigate the numerical solutions of several fractional-order models of the multi-space coupled Korteweg–De Vries equation involving many different kernels. In order to transform these models into a set...

  • Article
  • Open Access
25 Citations
2,176 Views
19 Pages

A primary aim of this study is to examine and simulate a fractional Coronavirus disease model by providing an efficient method for solving numerically this important model. In the Liouville-Caputo sense, the examined model consists of five fractional...

  • Article
  • Open Access
1 Citations
1,269 Views
12 Pages

18 October 2024

This article aims to explore the existence and stability of solutions to differential equations involving a ψ-Hilfer fractional derivative in the Caputo sense, which, compared to classical ψ-Hilfer fractional derivatives (in the Riemann&ndash...

  • Review
  • Open Access
108 Citations
8,746 Views
21 Pages

Several fractional-order operators are available and an in-depth knowledge of the selected operator is necessary for the evaluation of fractional integrals and derivatives of even simple functions. In this paper, we reviewed some of the most commonly...

  • Article
  • Open Access
1 Citations
1,010 Views
32 Pages

Regularity Results for Hybrid Proportional Operators on Hölder Spaces

  • Mieczysław Cichoń,
  • Hussein A. H. Salem and
  • Wafa Shammakh

Recently, a new type of derivative has been introduced, known as Caputo proportional derivatives. These are motivated by the applications of such derivatives (which are a generalization of Caputo’s standard fractional derivative) and the need t...

  • Article
  • Open Access
540 Views
25 Pages

20 June 2025

This paper is concerned with the investigation of a nonlocal sequential multistrip boundary-value problem for fractional differential inclusions, involving (k1,ψ1)-Hilfer and (k2,ψ2)-Caputo fractional derivative operators, and (k2,ψ2)- Ri...

  • Article
  • Open Access
11 Citations
2,926 Views
14 Pages

Enhancing the Accuracy of Solving Riccati Fractional Differential Equations

  • Antonela Toma,
  • Flavius Dragoi and
  • Octavian Postavaru

In this paper, we solve Riccati equations by using the fractional-order hybrid function of block-pulse functions and Bernoulli polynomials (FOHBPB), obtained by replacing x with xα, with positive α. Fractional derivatives are in the Caput...

  • Article
  • Open Access
1,018 Views
28 Pages

15 November 2024

We analyze the error estimates of a fully discrete scheme for solving a semilinear stochastic subdiffusion problem driven by integrated fractional Gaussian noise with a Hurst parameter H∈(0,1). The covariance operator Q of the stochastic fractio...

  • Article
  • Open Access
1 Citations
1,982 Views
15 Pages

Combined Liouville–Caputo Fractional Differential Equation

  • McSylvester Ejighikeme Omaba,
  • Hamdan Al Sulaimani,
  • Soh Edwin Mukiawa,
  • Cyril Dennis Enyi and
  • Tijani Abdul-Aziz Apalara

This paper studies a fractional differential equation combined with a Liouville–Caputo fractional differential operator, namely, LCDηβ,γQ(t)=λϑ(t,Q(t)),t∈[c,d],β,γ∈(0,1],η∈[0,1], wher...

  • Article
  • Open Access
24 Citations
3,558 Views
12 Pages

Novel Fractional Models Compatible with Real World Problems

  • Ramazan Ozarslan,
  • Ahu Ercan and
  • Erdal Bas

In this paper, some real world modeling problems: vertical motion of a falling body problem in a resistant medium, and the Malthusian growth equation, are considered by the newly defined Liouville–Caputo fractional conformable derivative and the modi...

  • Article
  • Open Access
59 Citations
5,743 Views
19 Pages

6 March 2019

In this work, we investigate a series of mathematical aspects for the fractional diffusion equation with stochastic resetting. The stochastic resetting process in Evans–Majumdar sense has several applications in science, with a particular empha...

  • Article
  • Open Access
4 Citations
1,914 Views
11 Pages

Univariate and Multivariate Ostrowski-Type Inequalities Using Atangana–Baleanu Caputo Fractional Derivative

  • Henok Desalegn Desta,
  • Deepak B. Pachpatte,
  • Jebessa B. Mijena and
  • Tadesse Abdi

19 September 2022

In this paper, we obtain some univariate and multivariate Ostrowski-type inequalities using the Atangana–Baleanu fractional derivative in the sense of Liouville–Caputo (ABC). The results obtained for both left and right ABC fractional der...

  • Article
  • Open Access
22 Citations
2,349 Views
12 Pages

Modified Fractional Difference Operators Defined Using Mittag-Leffler Kernels

  • Pshtiwan Othman Mohammed,
  • Hari Mohan Srivastava,
  • Dumitru Baleanu and
  • Khadijah M. Abualnaja

25 July 2022

The discrete fractional operators of Riemann–Liouville and Liouville–Caputo are omnipresent due to the singularity of the kernels. Therefore, convexity analysis of discrete fractional differences of these types plays a vital role in maint...

  • Article
  • Open Access
2 Citations
379 Views
16 Pages

Chaos and Bifurcations in the Dynamics of the Variable-Order Fractional Rössler System

  • Athar I. Ahmed,
  • Mohamed Elbadri,
  • Naseam Al-kuleab,
  • Dalal M. AlMutairi,
  • Nidal E. Taha and
  • Mohammed E. Dafaalla

18 November 2025

This article investigates the chaotic features of a novel variable-order fractional Rössler system built with Liouville–Caputo derivatives of variable order. Variable-order fractional (VOF) operators incorporated in the system render its d...