Special Issue: Recent Advances in Fractional Calculus with Real World Applications

Guest Editors

Prof. Zakia Hammouch
FST Errachidia, Moulay Ismail University, Morocco
Email: z.hammouch@fste.umi.ac.ma


Prof. Dumitru Baleanu
Institute of Space Sciences, Romania and Cankaya University, Ankara, Turkey
Email: dumitru@cankaya.edu.tr


Manuscript Topics

In recent years, the fractional calculus has become a valuable tool for the modeling analysis and played a very important role in various fields such as: physics, chemistry, mechanics, electricity, biology, economy and control theory. Moreover, research on fractional ordinary or partial differential equations and other relative topics is very active and extensive around the world.


The focus will be on review new developments based on the fractional differentiation and integration, both on theoretical and numerical aspects.


This special session is a place for researchers to share new ideas on the theories, applications, numerical methods and simulations of fractional calculus and fractional differential equations. Our interested topics, but not limited, are given below


• New analytical and numerical methods to solve fractional differential equations
• Deterministic and stochastic fractional-order models
• Computational methods for fractional differential equations
• Analysis, modeling and control of fractional-order of phenomena in:
— Fluids dynamics;
— Mechanics;
— Biology;
— Physics;
— Optical Solitons
— Lie Symmetries
— Stability Analysis


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Please submit your manuscript to online submission system
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Paper Submission

All manuscripts will be peer-reviewed before their acceptance for publication. The deadline for manuscript submission is 11 March 2019

Published Papers(25)

Research article
Spectral structure and solution of fractional hydrogen atom difference equations
Erdal Bas Ramazan Ozarslan Resat Yilmazer
2020, Volume 5, Issue 2: 1359-1371. doi: 10.3934/math.2020093
Abstract HTML PDF Cited (4) Viewed (3883)
Research article
Investigating of an immune system-cancer mathematical model with Mittag-Leffler kernel
Necati Özdemir Esmehan Uçar
2020, Volume 5, Issue 2: 1519-1531. doi: 10.3934/math.2020104
Abstract HTML PDF Cited (31) Viewed (4724)
Research article
Fractional order SIR model with generalized incidence rate
Muhammad Altaf Khan Muhammad Ismail Saif Ullah Muhammad Farhan
2020, Volume 5, Issue 3: 1856-1880. doi: 10.3934/math.2020124
Abstract HTML PDF Cited (33) Viewed (5613)
Research article
On deferred statistical convergence of sequences of sets
Mikail Et M. Çagri Yilmazer
2020, Volume 5, Issue 3: 2143-2152. doi: 10.3934/math.2020142
Abstract HTML PDF Cited (11) Viewed (3770)
Research article
Caputo-Hadamard fractional differential equations with nonlocal fractional integro-differential boundary conditions via topological degree theory
Choukri Derbazi Hadda Hammouche
2020, Volume 5, Issue 3: 2694-2709. doi: 10.3934/math.2020174
Abstract HTML PDF Cited (17) Viewed (4491)
Research article
Parameter estimation and fractional derivatives of dengue transmission model
Windarto Muhammad Altaf Khan Fatmawati
2020, Volume 5, Issue 3: 2758-2779. doi: 10.3934/math.2020178
Abstract HTML PDF Cited (26) Viewed (6092)
Research article
A mathematical model of tuberculosis (TB) transmission with children and adults groups: A fractional model
Fatmawati Muhammad Altaf Khan Ebenezer Bonyah Zakia Hammouch Endrik Mifta Shaiful
2020, Volume 5, Issue 4: 2813-2842. doi: 10.3934/math.2020181
Abstract HTML PDF Cited (54) Viewed (7657)
Research article
A numerical study of the ferromagnetic flow of Carreau nanofluid over a wedge, plate and stagnation point with a magnetic dipole
H. Thameem Basha R. Sivaraj A. Subramanyam Reddy Ali J. Chamkha H. M. Baskonus
2020, Volume 5, Issue 5: 4197-4219. doi: 10.3934/math.2020268
Abstract HTML PDF Cited (38) Viewed (5683)
Research article
Generalized conformable variational calculus and optimal control problems with variable terminal conditions
Beyza Billur İskender Eroǧlu Dilara Yapışkan
2020, Volume 5, Issue 2: 1105-1126. doi: 10.3934/math.2020077
Abstract HTML PDF Cited (7) Viewed (4559)
Research article
Simpson’s type integral inequalities for ĸ-fractional integrals and their applications
Saima Rashid Ahmet Ocak Akdemir Fahd Jarad Muhammad Aslam Noor Khalida Inayat Noor
2019, Volume 4, Issue 4: 1087-1100. doi: 10.3934/math.2019.4.1087
Abstract HTML PDF Cited (35) Viewed (4425)
Research article
Travelling wave solutions for fractional Korteweg-de Vries equations via an approximate-analytical method
Hayman Thabet Subhash Kendre James Peters
2019, Volume 4, Issue 4: 1203-1222. doi: 10.3934/math.2019.4.1203
Abstract HTML PDF Cited (16) Viewed (5265)
Research article
A new numerical technique for solving Caputo time-fractional biological population equation
Ali Khalouta Abdelouahab Kadem
2019, Volume 4, Issue 5: 1307-1319. doi: 10.3934/math.2019.5.1307
Abstract HTML PDF Cited (8) Viewed (4461)
Research article
New solitary wave solutions and stability analysis of the Benney-Luke and the Phi-4 equations in mathematical physics
Behzad Ghanbari Mustafa Inc Abdullahi Yusuf Dumitru Baleanu
2019, Volume 4, Issue 6: 1523-1539. doi: 10.3934/math.2019.6.1523
Abstract HTML PDF Cited (38) Viewed (4563)
Research article
Ostrowski type inequalities via new fractional conformable integrals
Erhan Set Ahmet Ocak Akdemir Abdurrahman Gözpınar Fahd Jarad
2019, Volume 4, Issue 6: 1684-1697. doi: 10.3934/math.2019.6.1684
Abstract HTML PDF Cited (12) Viewed (4370)
Research article
A new computational for approximate analytical solutions of nonlinear time-fractional wave-like equations with variable coefficients
Ali Khalouta Abdelouahab Kadem
2020, Volume 5, Issue 1: 1-14. doi: 10.3934/math.2020001
Abstract HTML PDF Cited (9) Viewed (5181)
Research article
The existence and uniqueness of solution for linear system of mixed Volterra-Fredholm integral equations in Banach space
Pakhshan M. Hasan Nejmaddin A. Sulaiman Fazlollah Soleymani Ali Akgül
2020, Volume 5, Issue 1: 226-235. doi: 10.3934/math.2020014
Abstract HTML PDF Cited (5) Viewed (5735)
Research article
On the fractional model of Fokker-Planck equations with two different operator
Zeliha Korpinar Mustafa Inc Dumitru Baleanu
2020, Volume 5, Issue 1: 236-248. doi: 10.3934/math.2020015
Abstract HTML PDF Cited (13) Viewed (4883)
Research article
Fractional physical problems including wind-influenced projectile motion with Mittag-Leffler kernel
Ramazan Ozarslan Erdal Bas Dumitru Baleanu Bahar Acay
2020, Volume 5, Issue 1: 467-481. doi: 10.3934/math.2020031
Abstract HTML PDF Cited (23) Viewed (5311)
Research article
New reproducing kernel functions in the reproducing kernel Sobolev spaces
Ali Akgül Esra Karatas Akgül Sahin Korhan
2020, Volume 5, Issue 1: 482-496. doi: 10.3934/math.2020032
Abstract HTML PDF Cited (5) Viewed (4767)
Research article
Complex solitons in the conformable (2+1)-dimensional Ablowitz-Kaup-Newell-Segur equation
Wei Gao Gulnur Yel Haci Mehmet Baskonus Carlo Cattani
2020, Volume 5, Issue 1: 507-521. doi: 10.3934/math.2020034
Abstract HTML PDF Cited (163) Viewed (8132)
Research article
Optical solitons for Triki-Biswas equation by two analytic approaches
Aliyu Isa Aliyu Ali S. Alshomrani Mustafa Inc Dumitru Baleanu
2020, Volume 5, Issue 2: 1001-1010. doi: 10.3934/math.2020069
Abstract HTML PDF Cited (20) Viewed (4786)
Research article
Existence and uniqueness of miscible flow equation through porous media with a non singular fractional derivative
Ritu Agarwal Mahaveer Prasad Yadav Dumitru Baleanu S. D. Purohit
2020, Volume 5, Issue 2: 1062-1073. doi: 10.3934/math.2020074
Abstract HTML PDF Cited (33) Viewed (4643)
Research article
A new approach to solve Cattaneo-Hristov diffusion model and fractional diffusion equations with Hilfer-Prabhakar derivative
Yudhveer Singh Devendra Kumar Kanak Modi Vinod Gill
2020, Volume 5, Issue 2: 843-855. doi: 10.3934/math.2020057
Abstract HTML PDF Viewed (2922)
Research article
New extensions of Chebyshev-Pólya-Szegö type inequalities via conformable integrals
Erhan Deniz Ahmet Ocak Akdemir Ebru Yüksel
2020, Volume 5, Issue 2: 956-965. doi: 10.3934/math.2020066
Abstract HTML PDF Cited (7) Viewed (3848)
Research article
A reliable hybrid numerical method for a time dependent vibration model of arbitrary order
Amit Prakash Manish Goyal Haci Mehmet Baskonus Shivangi Gupta
2020, Volume 5, Issue 2: 979-1000. doi: 10.3934/math.2020068
Abstract HTML PDF Cited (37) Viewed (4288)