• The (k, s) -fractional calculus of k-Mittag-Leffler function 

  Nisar, Ks; Rahman, G.; Baleanu, D.; Mubeen, S.; Arshad, M. (2017-12-01)

  In this paper, we introduce the (k, s) -fractional integral and differential operators involving k-Mittag-Leffler function Ek,ρ,βδ(z) as its kernel. Also, we establish various properties of these operators. Further, we ...
• Novel precise solutions and bifurcation of traveling wave solutions for the nonlinear fractional (3 + 1) -dimensional WBBM equation 

  Siddique, Imran; Mehdi, Khush Bukht; Jarad, Fahd; Elbrolosy, Mamdouh E.; Elmandouh, Adel A. (2023-01-20)

  The nonlinear fractional differential equations (FDEs) are composed by mathematical modeling through nonlinear corporeal structures. The study of these kinds of models has an energetic position in different fields of applied ...
• The (2 + 1)-dimensional Heisenberg ferromagnetic spin chain equation: its solitons and Jacobi elliptic function solutions 

  Hosseini, Kamyar; Salahshour, Soheil; Mirzazadeh, Mohammad; Ahmadian, Ali; Baleanu, Dumitru; Khoshrang, Arian (2021-02)

  The search for exact solutions of nonlinear evolution models with different wave structures has achieved significant attention in recent decades. The present paper studies a nonlinear (2 + 1)-dimensional evolution model ...
• Novel numerical investigation of the fractional oncolytic effectiveness model with M1 virus via generalized fractional derivative with optimal criterion 

  Rashid, Saima; Khalid, Aasma; Sultana, Sobia; Jarad, Fahd; Abualnaja, Khadijah M.; Hamed, Y.S. (2022-06)

  Oncolytic virotherapy is an efficacious chemotherapeutic agent that addresses and eliminates cancerous tissues by employing recombinant infections. M1 is a spontaneously produced oncolytic alphavirus with exceptional ...
• Nonlinear wave train in an inhomogeneous medium with the fractional theory in a plane self-focusing 

  Asjad, Muhammad Imran; Faridi, Waqas Ali; Jhangeer, Adil; Aleem, Maryam; Yusuf, Abdullahi; Alshomrani, Ali S.; Baleanu, Dumitru (2022)

  The aim of study is to investigate the Hirota equation which has a significant role in applied sciences, like maritime, coastal engineering, ocean, and the main source of the environmental action due to energy transportation ...
• Non-linear soliton solutions of perturbed Chen-Lee-Liu model by Φ 6- model expansion approach 

  Faridi, Waqas Ali; Asjad, Muhammad Imran; Jarad, Fahd (2022-10)

  This study deals with the perturbed Chen-Lee-Liu governing mode which portrays the propagating phenomena of the optical pulses in the discipline of optical fiber and plasma. The Cauchy problem for this equation cannot be ...
• Nonlinear realization of the script N = 2, D = 6 supergravity 

  Yılmaz, Nejat T. (2007-01-10)

  We have applied the method of dualization to construct the coset realization of the bosonic sector of the script N = 2, D = 6 supergravity which is coupled to a tensor multiplet. The bosonic field equations are regained ...
• Nonlinear higher order fractional terminal value problems 

  Baleanu, Dumitru; Shiri, Babak (2022)

  Terminal value problems for systems of fractional differential equations are studied with an especial focus on higher-order systems. Discretized piecewise polynomial collocation methods are used for approximating the exact ...
• Nonlinear dynamics and chaos in fractional differential equations with a new generalized Caputo fractional derivative 

  Odibat, Zaid; Baleanu, Dumitru (2022-06)

  In this paper, novel systems of fractional differential equations involving a new generalized Caputo fractional derivative were proposed. The complex dynamic behavior of these systems was studied by numerical simulation. ...
• Non-instantaneous impulsive fractional-order delay differential systems with Mittag-Leffler kernel 

  Kavitha, Velusamy; Arjunan, Mani Mallika; Baleanu, Dumitru (2022)

  The existence of fractional-order functional differential equations with non-instantaneous impulses within the Mittag-Leffler kernel is examined in this manuscript. Non-instantaneous impulses are involved in such equations ...
• Non-Instantaneous Impulsive Fractional Integro-Differential Equations with State-Dependent Delay 

  Benkhettou, Nadia; Salim, Abdelkrim; Aissani, Khalida; Benchohra, Mouffak; Karapınar, Erdal (2022-09)

  This paper deals with the existence and uniqueness of the mild solution of the fractional integro-differential equations with non-instantaneous impulses and state-dependent delay. Our arguments are based on the fixed point ...
• New Solutions of Nonlinear Dispersive Equation in Higher-Dimensional Space with Three Types of Local Derivatives 

  Akgül, Ali; Hashemi, Mir Sajjad; Jarad, Fahd (2022-04)

  The aim of this paper is to use the Nucci’s reduction method to obtain some novel exact solutions to the s-dimensional generalized nonlinear dispersive mK(m,n) equation. To the best of the authors’ knowledge, this paper ...
• New results for a coupled system of abr fractional differential equations with sub-strip boundary conditions 

  Almalahi, Mohammed A.; Panchal, Satish K.; Aljaaidi, Tariq A.; Jarad, Fahd (2022)

  In this article, we investigate sufficient conditions for the existence, uniqueness and Ulam-Hyers (UH) stability of solutions to a new system of nonlinear ABR fractional derivative of order 1 < ϱ ≤ 2 subjected to multi-point ...
• New numerical dynamics of the heroin epidemic model using a fractional derivative with Mittag-Leffler kernel and consequences for control mechanisms 

  Rashid, Saima; Jarad, Fahd; Ahmad, Abdulaziz Garb; Abualnaja, Khadijah M. (2022-04)

  Intravenous substance consumption is on the upswing all over the globe, especially in Europe and Asia. It is extremely harmful to society; excessive substance consumption is the leading cause of death. Beyond all prohibited ...
• New Multi-Functional Approach For Κ Th-Order Differentiability Governed By Fractional Calculus Via Approximately Generalized (Ψ, ?) -Convex Functions İn Hilbert Space 

  Wang, Miao-Kun; Rashid, Saima; Karaca, Yeliz; Chu, Yu-Ming (2021-08)

  This work addresses several novel classes of convex function involving arbitrary non-negative function, which is known as approximately generalized (ψ, ?)-convex and approximately ψ-quasiconvex function, with respect to ...
• New Estimates of q1q2 -Ostrowski-Type Inequalities within a Class of n -Polynomial Prevexity of Functions 

  Kalsoom, Humaira; Idrees, Muhammad; Baleanu, Dumitru; Chu, Yu-Ming (2020)

  In this article, we develop a novel framework to study for a new class of preinvex functions depending on arbitrary nonnegative function, which is called n-polynomial preinvex functions. We use the n-polynomial preinvex ...
• New classifications of monotonicity investigation for discrete operators with Mittag-Leffler kernel 

  Mohammed, Pshtiwan Othman; Goodrich, Christopher S.; Brzo, Aram Bahroz; Baleanu, Dumitru; Hamed, Yasser S. (2022)

  This paper deals with studying monotonicity analysis for discrete fractional operators with Mittag-Leffler in kernel. The ν-monotonicity definitions, namely ν-(strictly) increasing and ν-(strictly) decreasing, are presented ...
• New approach on controllability of Hilfer fractional derivatives with nondense domain 

  Nisar, Kottakkaran Sooppy; Jothimani, Kasthurisamy; Ravichandran, Chokkalingam; Baleanu, Dumitru; Kumar, Devendra (2022)

  This work picturizes the results on the controllability of the nondense Hilfer neutral fractional derivative (HNFD). The uniqueness and controllability of HNFD are discussed with Mönch theorem and Banach contraction ...
• New applications related to hepatitis C model 

  Ahmed, Nauman; Raza, Ali; Akgül, Ali; Iqbal, Zafar; Rafiq, Muhammad; Ahmad, Muhammad Ozair; Jarad, Fahd (2022)

  The main idea of this study is to examine the dynamics of the viral disease, hepatitis C. To this end, the steady states of the hepatitis C virus model are described to investigate the local as well as global stability. ...
• New analytical wave structures for the (3 + 1)-dimensional Kadomtsev-Petviashvili and the generalized Boussinesq models and their applications 

  Lu, D.; Tariq, K.U.; Osman, M.S.; Baleanu, Dumitru; Younis M., Younis M; Khater, M.M.A. (2019-09)

  Different types of soliton wave solutions for the (3 + 1)-dimensional Kadomtsev-Petviashvili and the generalized Boussinesq equations are investigated via the solitary wave ansatz method. These solutions are classified ...

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