• SOME SYMMETRIC PROPERTIES AND APPLICATIONS OF WEIGHTED FRACTIONAL INTEGRAL OPERATOR 

  Wu, Shanhe; Samraiz, Muhammad; Mehmood, Ahsan; Jarad, Fahd; Naheed, Saima (2023)

  In this paper, a weighted generalized fractional integral operator based on the Mittag-Leffler function is established, and it exhibits symmetric characteristics concerning classical operators. We demonstrate the semigroup ...
• Some more bounded and singular pulses of a generalized scale-invariant analogue of the Korteweg–de Vries equation 

  Saifullah, Sayed; Alqarni, M.M.; Ahmad, Shabir; Baleanu, Dumitru; Khan, Meraj Ali; Mahmoud, Emad E. (2023-09)

  We investigate a generalized scale-invariant analogue of the Korteweg–de Vries (KdV) equation, establishing a connection with the recently discovered short-wave intermediate dispersive variable (SIdV) equation. To conduct ...
• Solving System of Fractional Differential Equations via Vieta-Lucas Operational Matrix Method 

  Chaudhary, Rahul; Aeri, Shivani; Bala, Anu; Kumar, Rakesh; Baleanu, Dumitru (2024-02)

  Vieta-Lucas polynomials (VLPs) belong to the class of weighted orthogonal polynomials, which can be used to effectively handle various natural and engineered problems. The classical fractional derivative due to Caputo is ...
• Solving fractional integro-differential equations by Aboodh transform 

  Raghavendran, Prabakaran; Gunasekar, Tharmalingam; Balasundaram, Hemalatha; Santra, Shyam Sundar; Majumder, Debasish; Baleanu, Dumitru (2024)

  This study approaches some families of fractional integro-differential equations (FIDEs) using a simple fractional calculus method, which leads to several appealing consequences, including the classical Frobenius method, ...
• Solitons of the (1 + 1) - and (2 + 1) -Dimensional Chiral Nonlinear Schrodinger Equations with the Jacobi Elliptical Function Method 

  Tala-Tebue, Eric; Rezazadeh, Hadi; Javeed, Shumaila; Baleanu, Dumitru; Korkmaz, Alper (2023-09)

  Our objective is to find new analytical solutions of the (1 + 1) - and (2 + 1) -dimensional Chiral nonlinear Schrodinger (CNLS) equations using the Jacobi elliptical function method. The CNLS equations play a significant ...
• Solitary wave solutions to Gardner equation using improved tan(Ω(Υ)/2-expansion method 

  Akram, Ghazala; Sadaf, Maasoomah; Dawood, Mirfa; Abbas, Muhammad; Baleanu, Dumitru (2023)

  In this study, the improved tan(Ω(Υ)/2-expansion method is used to construct a variety of precise soliton and other solitary wave solutions of the Gardner equation. Gardner equation is extensively utilized in plasma physics, ...
• Simulating systems of Ito? SDEs with split-step (?, ?)-Milstein scheme 

  Ranjbar, Hassan; Torkzadeh, Leila; Baleanu, Dumitru; Nouri, Kazem (2022)

  In the present study, we provide a new approximation scheme for solving stochastic differential equations based on the explicit Milstein scheme. Under sufficient conditions, we prove that the split-step (alpha, beta)-Milstein ...
• Recent developments of energy management strategies in microgrids: An updated and comprehensive review and classification 

  Abbasi, Ali Reza; Baleanu, Dumitru (2023-12-01)

  Energy is one of the essential foundations for the sustainable development of human society, so its management is necessary. Energy management system (EMS) can be explained as the procedure of optimizing, planning, ...
• Quasilinear Coupled System in the Frame of Nonsingular ABC-Derivatives with p-Laplacian Operator at Resonance 

  Bouloudene, Mokhtar; Jarad, Fahd; Adjabi, Yassine; Panda, Sumati Kumari (2024-02)

  We investigate the existence of solutions for coupled systems of fractional p-Laplacian quasilinear boundary value problems at resonance given by the Atangana–Baleanu–Caputo (shortly, ABC) derivatives formulations are based ...
• Preface to the Special Issue “A Themed Issue on Mathematical Inequalities, Analytic Combinatorics and Related Topics in Honor of Professor Feng Qi” 

  Du, Wei-Shih; Agarwal, Ravi Prakash; Karapinar, Erdal; Kostić, Marko; Cao, Jian (2023-09)
• Pathological study on uncertain numbers and proposed solutions for discrete fuzzy fractional order calculus 

  Shiri, Babak; Baleanu, Dumitru; Ma, Chang-You (2023-01-01)

  A pathological study in the definition of uncertain numbers is carried out, and some solutions are proposed. Fundamental theorems for uncertain discrete fractional and integer order calculus are established. The concept ...
• Pachpatte type inequalities and their nabla unifications via convexity 

  Kayar, Zeynep; Kaymakçalan, Billur (2024)

  Nabla unifications of the discrete and continuous Pachpatte type inequalities, which are convex generalizations of Hardy-Copson type inequalities, are established. These unifications also yield dual results, namely delta ...
• Optimal control for a variable-order diffusion-wave equation with a reaction term; A numerical study 

  Sweilam, N.H.; Megahed, F.; Shatta, S.A.; Baleanu, Dumitru (2024-06)

  In this paper, optimal control for a variable-order diffusion-wave equation with a reaction term is numerically studied, where the variable-order operator is defined in the sense of Caputo proportional constant. Necessary ...
• On Weighted Fractional Operators with Applications to Mathematical Models Arising in Physics 

  Samraiz, Muhammad; Umer, Muhammad; Naheed, Saima; Baleanu, Dumitru (2023)

  In recent study, we develop the weighted generalized Hilfer-Prabhakar fractional derivative operator and explore its key properties. It unifies many existing fractional derivatives like Hilfer-Prabhakar and Riemann-Liouville. ...
• On the multiparameterized fractional multiplicative integral inequalities 

  Almatrafi, Mohammed Bakheet; Saleh, Wedad; Lakhdari, Abdelghani; Jarad, Fahd (2024-12)

  We introduce a novel multiparameterized fractional multiplicative integral identity and utilize it to derive a range of inequalities for multiplicatively s-convex mappings in connection with different quadrature rules ...
• On the Maximal Subspaces of Discrete Hamiltonian Systems 

  Uğurlu, Ekin; Bairamov, Elgiz (2024-05)

  In this paper, we consider a discrete Hamiltonian system on nonnegative integers, and using Sylvester’s inertia indices theory, we construct maximal subspaces on which the Hermitian form has a certain sign. After constructing ...
• On the decomposition and analysis of novel simultaneous SEIQR epidemic model 

  Umapathy, Kalpana; Palanivelu, Balaganesan; Jayaraj, Renuka; Baleanu, Dumitru; Dhandapani, Prasantha Bharathi (2023)

  In this manuscript, we are proposing a new kind of modified Susceptible Exposed Infected Quarantined Recovered model (SEIQR) with some assumed data. The novelty imposed here in the study is that we are studying simultaneously ...
• On the complementary nabla Pachpatte type dynamic inequalities via convexity 

  Kayar, Zeynep; Kaymakçalan, Billur (2024-01)

  Pachpatte type inequalities are convex generalizations of the well-known Hardy-Copson type inequalities. As Hardy-Copson type inequalities and convexity have numerous applications in pure and applied mathematics, combining ...
• On the characteristic functions and Dirchlet-integrable solutions of singular left-definite Hamiltonian systems 

  Bairamov, Elgiz; Taş, Kenan; Uğurlu, Ekin (2024)

  In this work, a singular left-definite Hamiltonian system is considered and the characteristic-matrix theory for this Hamiltonian system is constructed. Using the results of this theory we introduce a lower bound for the ...
• On some even-sequential fractional boundary-value problems 

  Uğurlu, Ekin (2024-02)

  In this paper we provide a way to handle some symmetric fractional boundary-value problems. Indeed, first, we consider some system of fractional equations. We introduce the existence and uniqueness of solutions of the ...

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