Positive Solvability for Conjugate Fractional Differential Inclusion of (<i>k</i>, <i>n</i> − <i>k</i>) Type without Continuity and Compactness

• Main Authors: Ahmed Salem, Aeshah Al-Dosari
• Format: Article
• Language: English
• Published: MDPI AG 2021-07-01
• Series: Axioms
• Subjects: (<i>n</i> − <i>k</i>, <i>k</i>) conjugate operator; existence and uniqueness; monotone operator; spectral radius
• Online Access: https://www.mdpi.com/2075-1680/10/3/170
• ISSN: 2075-1680

The monotonicity of multi-valued operators serves as a guideline to prove the existence of the results in this article. This theory focuses on the existence of solutions without continuity and compactness conditions. We study these results for the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>k</mi><mo>,</mo><mspace width="3.33333pt"></mspace><mi>n</mi><mo>−</mo><mi>k</mi><mo>)</mo></mrow></semantics></math></inline-formula> conjugate fractional differential inclusion type with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="sans-serif">λ</mi><mo>></mo><mn>0</mn><mo>,</mo><mspace width="3.33333pt"></mspace><mn>1</mn><mo>≤</mo><mi>k</mi><mo>≤</mo><mi>n</mi><mo>−</mo><mn>1</mn></mrow></semantics></math></inline-formula>.