Special Issue "Recent Trends in Computational Methods for Differential Equations"

Submission Deadline: 01 June 2021 (closed)
Guest Editors
Dr. Hijaz Ahmad, University of Engineering and Technology Peshawar, Pakistan / International Telematic University Uninettuno, Italy.
Dr. M. Atif, King Saud University, Saudi Arabia.
Dr. Ali Akgül, Siirt University, Turkey.
Dr. Zareen A Khan, Princess Nourah bint Abdulrahman University, Saudi Arabia.
Dr. Saima Rashid, Government College University, Pakistan.


Fractional calculus has been an important area of applied mathematics in the last few decades. The modeling of real phenomena with fractional derivative and fractional integral delivers better results than classical orders. Some interesting applications can be traced in modeling some physical phenomena, especially signal processing, electronics, the damping viscoelasticity, communication, genetic algorithms, robotics, transport systems, chemistry, biology, physics and finance. Several researchers are working on some important developments and contributions in the field of fractional calculus. Due to its intriguing uses, fractional calculus is a significant area of research for most analysts and researchers and the study of fractional order partial differential equations (PDEs) have received particular interest from numerous researchers. In light of this, various linear and nonlinear fractional PDE has been solved using a variety of methods. On the other hand, fractional derivatives can be utilized to model a variety of interdisciplinary problems. However, it is hard to find exact solutions of these types fractional-order differential equations. Therefore, numerical and approximate methods can be used for its treatment.

This Special Issue deals with the recent advances in numerical techniques for partial differential equations of integer order as well as fractional-order, especially in science and engineering, and will accept high-quality papers having original research results.

• Fractional Differential Equations
• Fractional Difference Equations
• Fractional Functional Differential Systems
• New analytical and numerical methods for fractional differential equations
• Fractals and related topics
• Fractional Impulsive Systems
• Fractional Uncertain Systems
• Fuzzy differential equations and their applications
• Fractal signal processing and applications
• Fractional Control Problem
• Fractional Modelling to Real-World PhenomenaFractal Derivatives

Published Papers
  • A Novel COVID-19 Prediction Model with Optimal Control Rates
  • Abstract The Corona (COVID-19) epidemic has triggered interest in many fields of technology, medicine, science, and politics. Most of the mathematical research in this area focused on analyzing the dynamics of the spread of the virus. In this article, after a review of some current methodologies, a non-linear system of differential equations is developed to model the spread of COVID-19. In order to consider a wide spectrum of scenarios, we propose a susceptible-exposed-infected-quarantined-recovered (SEIQRS)-model which was analyzed to determine threshold conditions for its stability, and the number of infected cases that is an infected person will transmit on a virus to,… More
  •   Views:626       Downloads:349       Cited by:1        Download PDF

  • Periodic Solutions for Two Dimensional Quartic Non-Autonomous Differential Equation
  • Abstract In this article, the maximum possible numbers of periodic solutions for the quartic differential equation are calculated. In this regard, for the first time in the literature, we developed new formulae to determine the maximum number of periodic solutions greater than eight for the quartic equation. To obtain the maximum number of periodic solutions, we used a systematic procedure of bifurcation analysis. We used computer algebra Maple 18 to solve lengthy calculations that appeared in the formulae of focal values as integrations. The newly developed formulae were applied to a variety of polynomials with algebraic and homogeneous trigonometric coefficients of… More
  •   Views:612       Downloads:387        Download PDF

  • An Optimized Scale-Invariant Feature Transform Using Chamfer Distance in Image Matching
  • Abstract Scale-Invariant Feature Transform is an image matching algorithm used to match objects of two images by extracting the feature points of target objects in each image. Scale-Invariant Feature Transform suffers from long processing time due to embedded calculations which reduces the overall speed of the technique. This research aims to enhance SIFT processing time by imbedding Chamfer Distance Algorithm to find the distance between image descriptors instead of using Euclidian Distance Algorithm used in SIFT. Chamfer Distance Algorithm requires less computational time than Euclidian Distance Algorithm because it selects the shortest path between any two points when the distance is… More
  •   Views:700       Downloads:423        Download PDF

  • Optimal Control and Spectral Collocation Method for Solving Smoking Models
  • Abstract In this manuscript, we solve the ordinary model of nonlinear smoking mathematically by using the second kind of shifted Chebyshev polynomials. The stability of the equilibrium point is calculated. The schematic of the model illustrates our proposition. We discuss the optimal control of this model, and formularize the optimal control smoking work through the necessary optimality cases. A numerical technique for the simulation of the control problem is adopted. Moreover, a numerical method is presented, and its stability analysis discussed. Numerical simulation then demonstrates our idea. Optimal control for the model is further discussed by clarifying the optimal control through… More
  •   Views:669       Downloads:500       Cited by:3        Download PDF

  • Cryptanalysis of an Online/Offline Certificateless Signature Scheme for Internet of Health Things
  • Abstract Recently, Khan et al. [An online-offline certificateless signature scheme for internet of health things,” Journal of Healthcare Engineering, vol. 2020] presented a new certificateless offline/online signature scheme for Internet of Health Things (IoHT) to fulfill the authenticity requirements of the resource-constrained environment of (IoHT) devices. The authors claimed that the newly proposed scheme is formally secured against Type-I adversary under the Random Oracle Model (ROM). Unfortunately, their scheme is insecure against adaptive chosen message attacks. It is demonstrated that an adversary can forge a valid signature on a message by replacing the public key. Furthermore, we performed a comparative analysis… More
  •   Views:770       Downloads:535        Download PDF

  • On Parametric Fuzzy Linear Programming Formulated by a Fractal
  • Abstract Fractal strategy is an important tool in manufacturing proposals, including computer design, conserving, power supplies and decorations. In this work, a parametric programming, analysis is proposed to mitigate an optimization problem. By employing a fractal difference equation of the spread functions (local fractional calculus operator) in linear programming, we aim to analyze the restraints and the objective function. This work proposes a new technique of fractal fuzzy linear programming (FFLP) model based on the symmetric triangular fuzzy number. The parameter fuzzy number is selected from the fractal power of the difference equation. Note that this number indicates the fractal parameter,… More
  •   Views:696       Downloads:505        Download PDF

  • Exact Analysis of Second Grade Fluid with Generalized Boundary Conditions
  • Abstract Convective flow is a self-sustained flow with the effect of the temperature gradient. The density is non-uniform due to the variation of temperature. The effect of the magnetic flux plays a major role in convective flow. The process of heat transfer is accompanied by mass transfer process; for instance condensation, evaporation and chemical process. Due to the applications of the heat and mass transfer combined effects in different field, the main aim of this paper is to do comprehensive analysis of heat and mass transfer of MHD unsteady second-grade fluid in the presence of time dependent generalized boundary conditions. The… More
  •   Views:971       Downloads:675       Cited by:6        Download PDF

  • Multi-Model Fuzzy Formation Control of UAV Quadrotors
  • Abstract In this paper, the formation control problem of a group of unmanned air vehicle (UAV) quadrotors is solved using the Takagi–Sugeno (T–S) multi-model approach to linearize the nonlinear model of UAVs. The nonlinear model sof the quadrotor is linearized first around a set of operating points using Taylor series to get a set of local models. Our approach’s novelty is in considering the difference between the nonlinear model and the linearized ones as disturbance. Then, these linear models are interpolated using the fuzzy T–S approach to approximate the entire nonlinear model. Comparison of the nonlinear and the T–S model shows… More
  •   Views:1284       Downloads:917        Download PDF