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Existence of positive solutions for weighted fractional order differential equations

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  • Abdo, Mohammed S.
  • Abdeljawad, Thabet
  • Ali, Saeed M.
  • Shah, Kamal
  • Jarad, Fahd

Abstract

In this paper, we deliberate two classes of initial value problems for nonlinear fractional differential equations under a version weighted generalized of Caputo fractional derivative given by Jarad et al. (2020a) [25]. We get a formula for the solution through the equivalent fractional integral equations to the proposed problems. The existence and uniqueness of positive solutions have been obtained by using lower and upper solutions. The acquired results are demonstrated by building the upper and lower control functions of the nonlinear term with the aid of Banach and Schauder fixed point theorems. The acquired results are demonstrated by pertinent numerical examples along with the Bashforth Moulton prediction correction scheme and Matlab.

Suggested Citation

  • Abdo, Mohammed S. & Abdeljawad, Thabet & Ali, Saeed M. & Shah, Kamal & Jarad, Fahd, 2020. "Existence of positive solutions for weighted fractional order differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    • Handle: RePEc:eee:chsofr:v:141:y:2020:i:c:s0960077920307360
    DOI: 10.1016/j.chaos.2020.110341
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    References listed on IDEAS

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    1. Atangana, Abdon, 2017. "Fractal-fractional differentiation and integration: Connecting fractal calculus and fractional calculus to predict complex system," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 396-406.
    2. Atangana, Abdon, 2020. "Fractional discretization: The African’s tortoise walk," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    3. Erden, Samet & Sarikaya, Mehmet Zeki, 2016. "Generalized Pompeiu type inequalities for local fractional integrals and its applications," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 282-291.
    4. Abdo, Mohammed S. & Shah, Kamal & Wahash, Hanan A. & Panchal, Satish K., 2020. "On a comprehensive model of the novel coronavirus (COVID-19) under Mittag-Leffler derivative," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    5. Mamadou Diouf & Ndolane Sene, 2020. "Analysis of the Financial Chaotic Model with the Fractional Derivative Operator," Complexity, Hindawi, vol. 2020, pages 1-14, June.
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    Cited by:

    1. Almalahi, Mohammed A. & Panchal, Satish K. & Jarad, Fahd, 2021. "Stability results of positive solutions for a system of ψ -Hilfer fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    2. Ahmad, Saeed & Rahman, Mati ur & Arfan, Muhammad, 2021. "On the analysis of semi-analytical solutions of Hepatitis B epidemic model under the Caputo-Fabrizio operator," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).

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