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  1. In this article, we present some new properties of the fractional proportional derivatives of a function with respect to a certain function. We use a modified Laplace transform to find the relation between the...

    Authors: Fahd Jarad, Thabet Abdeljawad, Saima Rashid and Zakia Hammouch

    Citation: Advances in Difference Equations 2020 2020:303

    Content type: Research

    Published on:

  2. In this manuscript, the existence of solutions for a novel category of the fractional differential equation of hybrid type with hybrid boundary value conditions is studied. Also, we review the existence result...

    Authors: S. Etemad, S. Pourrazi and Sh. Rezapour

    Citation: Advances in Difference Equations 2020 2020:302

    Content type: Research

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  3. It is well known that the Sturm–Liouville equation has many applications in different areas of science. Thus, it is important to review different versions of the well-known equation. The technique of α-admissible...

    Authors: Zohreh Zeinalabedini Charandabi, Shahram Rezapour and Mina Ettefagh

    Citation: Advances in Difference Equations 2020 2020:301

    Content type: Research

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  4. In this article, we deals with the existence and uniqueness of positive solutions of general non-linear fractional differential equations (FDEs) having fractional derivative of different orders involving p-Lap...

    Authors: Amita Devi, Anoop Kumar, Dumitru Baleanu and Aziz Khan

    Citation: Advances in Difference Equations 2020 2020:300

    Content type: Research

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  5. We present a fractional-order model for the COVID-19 transmission with Caputo–Fabrizio derivative. Using the homotopy analysis transform method (HATM), which combines the method of homotopy analysis and Laplac...

    Authors: Dumitru Baleanu, Hakimeh Mohammadi and Shahram Rezapour

    Citation: Advances in Difference Equations 2020 2020:299

    Content type: Research

    Published on:

  6. In this paper, we introduce the r-central factorial numbers with even indices of the first and second kind as extended versions of the central factorial numbers with even indices of both kinds. We obtain several ...

    Authors: F. A. Shiha

    Citation: Advances in Difference Equations 2020 2020:298

    Content type: Research

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  7. Integral operators have a very vital role in diverse fields of science and engineering. In this paper, we use φ-convex functions for unified integral operators to obtain their upper bounds and upper and lower bou...

    Authors: Young Chel Kwun, Moquddsa Zahra, Ghulam Farid, Saira Zainab and Shin Min Kang

    Citation: Advances in Difference Equations 2020 2020:297

    Content type: Research

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  8. In this paper, we aim to study a nonlocal Robin boundary value problem for fractional sequential fractional Hahn-q-equation. The existence and uniqueness results for this problem are revealed by using the Banach ...

    Authors: Thongchai Dumrongpokaphan, Nichaphat Patanarapeelert and Thanin Sitthiwirattham

    Citation: Advances in Difference Equations 2020 2020:294

    Content type: Research

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  9. We study the existence and nonexistence of positive solutions for a system of Riemann–Liouville fractional differential equations with p-Laplacian operators, nonnegative nonlinearities and positive parameters, su...

    Authors: Alexandru Tudorache and Rodica Luca

    Citation: Advances in Difference Equations 2020 2020:292

    Content type: Research

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  10. Recently, Wu (Mathematics 6(11):219, 2018; Mathematics 6(6):90, 2018) introduced the concept of a near-fixed point and established some results on near fixed points in a metric interval space and hyperspace. Moti...

    Authors: Misbah Ullah, Muhammad Sarwar, Hasib Khan, Thabet Abdeljawad and Aziz Khan

    Citation: Advances in Difference Equations 2020 2020:291

    Content type: Research

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  11. This paper proposes a new effective pseudo-spectral approximation to solve the Sylvester and Lyapunov matrix differential equations. The properties of the Chebyshev basis operational matrix of derivative are a...

    Authors: Kazem Nouri, Samaneh Panjeh Ali Beik, Leila Torkzadeh and Dumitru Baleanu

    Citation: Advances in Difference Equations 2020 2020:287

    Content type: Research

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  12. In this paper, we consider a class of Clifford-valued neutral-type neural networks with leakage delays on time scales. We do not decompose the networks under consideration into real-valued systems, but we dire...

    Authors: Shiping Shen and Yongkun Li

    Citation: Advances in Difference Equations 2020 2020:286

    Content type: Research

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  13. Temperature is one of the integral environmental drivers that strongly affect the distribution and density of tsetse fly population. Precisely, ectotherm performance measures, such as development rate, surviva...

    Authors: Mlyashimbi Helikumi, Moatlhodi Kgosimore, Dmitry Kuznetsov and Steady Mushayabasa

    Citation: Advances in Difference Equations 2020 2020:284

    Content type: Research

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  14. A numerical approach for solving second order singularly perturbed boundary value problems (SPBVPs) is introduced in this paper. This approach is based on the basis function of a 6-point interpolatory subdivis...

    Authors: Ghulam Mustafa, Syeda Tehmina Ejaz, Dumitru Baleanu, Abdul Ghaffar and Kottakkaran Sooppy Nisar

    Citation: Advances in Difference Equations 2020 2020:282

    Content type: Research

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  15. In this paper, we present some weakly compatible and quasi-contraction results for self-mappings in fuzzy cone metric spaces and prove some coincidence point and common fixed point theorems in the said space. ...

    Authors: Shamoona Jabeen, Saif Ur Rehman, Zhiming Zheng and Wei Wei

    Citation: Advances in Difference Equations 2020 2020:280

    Content type: Research

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  16. In this paper, we study boundary value problems, involving the Hilfer fractional derivative, for pantograph fractional differential equations and inclusions supplemented by nonlocal integral boundary condition...

    Authors: Athasit Wongcharoen, Sotiris K. Ntouyas and Jessada Tariboon

    Citation: Advances in Difference Equations 2020 2020:279

    Content type: Research

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  17. In this paper, by means of p-adic Volkenborn integrals we introduce and study two different degenerate versions of Bernoulli polynomials of the second kind, namely partially and fully degenerate Bernoulli polynom...

    Authors: Lee-Chae Jang, Dae San Kim, Taekyun Kim and Hyunseok Lee

    Citation: Advances in Difference Equations 2020 2020:278

    Content type: Research

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  18. In the article, we describe the Grüss type inequality, provide some related inequalities by use of suitable fractional integral operators, address several variants by utilizing the generalized proportional Had...

    Authors: Shuang-Shuang Zhou, Saima Rashid, Fahd Jarad, Humaira Kalsoom and Yu-Ming Chu

    Citation: Advances in Difference Equations 2020 2020:275

    Content type: Research

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  19. We investigate the existence of solutions for a Caputo–Hadamard fractional integro-differential equation with boundary value conditions involving the Hadamard fractional operators via different orders. By usin...

    Authors: Sina Etemad, Shahram Rezapour and Fethiye Muge Sakar

    Citation: Advances in Difference Equations 2020 2020:272

    Content type: Research

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  20. In this paper, we discuss the existence and uniqueness of solutions for a class of integral boundary value problems of nonlinear multi-term fractional differential equations and propose a new method to obtain ...

    Authors: KyuNam O, KumSong Jong, SunAe Pak and HuiChol Choi

    Citation: Advances in Difference Equations 2020 2020:271

    Content type: Research

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  21. We use an analytical scheme to construct distinct novel solutions of two well-known fractional complex models (the fractional Korteweg–de Vries equation (KdV) equation and the fractional Zakharov–Kuznetsov–Ben...

    Authors: Mostafa M. A. Khater and Dumitru Baleanu

    Citation: Advances in Difference Equations 2020 2020:268

    Content type: Research

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  22. In this article, several interesting properties of the incomplete I-functions associated with the Marichev–Saigo–Maeda (MSM) fractional operators are studied and investigated. It is presented that the order of th...

    Authors: Kamlesh Jangid, Sanjay Bhatter, Sapna Meena, Dumitru Baleanu, Maysaa Al Qurashi and Sunil Dutt Purohit

    Citation: Advances in Difference Equations 2020 2020:265

    Content type: Research

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  23. The celebrated Hermite–Hadamard and Ostrowski type inequalities have been studied extensively since they have been established. We find novel versions of the Hermite–Hadamard and Ostrowski type inequalities fo...

    Authors: Saima Rashid, İmdat İşcan, Dumitru Baleanu and Yu-Ming Chu

    Citation: Advances in Difference Equations 2020 2020:264

    Content type: Research

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  24. In this paper, certain Hermite–Hadamard–Mercer type inequalities are proved via k-Caputo fractional derivatives. We established some new k-Caputo fractional derivatives inequalities with Hermite–Hadamard–Mercer t...

    Authors: Shupeng Zhao, Saad Ihsan Butt, Waqas Nazeer, Jamshed Nasir, Muhammad Umar and Ya Liu

    Citation: Advances in Difference Equations 2020 2020:262

    Content type: Research

    Published on:

  25. In this paper, the development of new hybrid group iterative methods for the numerical solution of a two-dimensional time-fractional cable equation is presented. We use Laplace transform method to approximate ...

    Authors: Fouad Mohammad Salama, Norhashidah Hj. Mohd. Ali and Nur Nadiah Abd Hamid

    Citation: Advances in Difference Equations 2020 2020:257

    Content type: Research

    Published on:

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Editors-in-Chief

​​​​​​​mbnk_edit Martin Bohner, Missouri University of Science and Technology, United States of America | 

Martin's SpringerNature Publications

Elena_Braverman_image_edit Elena Braverman, University of Calgary Canada | 

Elena's SpringerNature Publications