Implicit fractional differential equation with anti-periodic boundary condition involving Caputo-Katugampola type

Saleh S. Redhwan; Sadikali L. Shaikh; Mohammed S. Abdo

doi:10.3934/math.2020240

AIMS Mathematics, 2020, 5(4): 3714-3730. doi: 10.3934/math.2020240. Research article

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Implicit fractional differential equation with anti-periodic boundary condition involving Caputo-Katugampola type

Saleh S. Redhwan, Sadikali L. Shaikh, Mohammed S. Abdo

1 Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University Aurangabad, (M.S), 431001, India
2 Department of Mathematics, Maulana Azad College of arts, Science and Commerce, RozaBagh, Aurangabad 431004 (M.S.), India
3 Department of Mathematics, Hodeidah University, Al-Hodeidah, Yemen

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This paper deals with a nonlinear implicit fractional differential equation with the anti-periodic boundary condition involving the Caputo-Katugampola type. The existence and uniqueness results are established by applying the fixed point theorems of Krasnoselskii and Banach. Further, by using generalized Gronwall inequality the Ulam-Hyers stability results are proved. To demonstrate the effectiveness of the main results, appropriate examples are granted.

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Keywords: fractional differential equations; Katugampola fractional operator; Ulam-Hyers stability; fixed point theorems; fractional Gronwall inequality

Citation: Saleh S. Redhwan, Sadikali L. Shaikh, Mohammed S. Abdo. Implicit fractional differential equation with anti-periodic boundary condition involving Caputo-Katugampola type. AIMS Mathematics, 2020, 5(4): 3714-3730. doi: 10.3934/math.2020240

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