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A partial fraction is a component of a rational expression represented as the sum of simpler fractions. When a rational function is expressed as a ratio of two polynomials, it can often be decomposed into a sum of fractions whose denominators are simpler polynomials, typically linear or irreducible quadratic factors. This process is called partial fraction decomposition, and it is used to simplify complex expressions for integration, solving equations, or analysis.Partial fraction decomposition...
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On two fractional differential inclusions.

Dumitru Baleanu1, Vahid Hedayati2, Shahram Rezapour2

  • 1Department of Mathematics, Cankaya University, Ogretmenler Cad. 14, 06530 Balgat, Ankara Turkey ; Institute of Space Sciences, Magurele, Bucharest, Romania.

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Summary
This summary is machine-generated.

This study explores the existence of solutions for fractional differential inclusions, including hybrid types. Researchers confirm solution existence and analyze solution set dimensions for these complex mathematical models.

Keywords:
Dimension solution setFixed pointFractional hybrid differential inclusions

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Area of Science:

  • Mathematics
  • Applied Mathematics
  • Fractional Calculus

Background:

  • Fractional differential inclusions are extensions of ordinary differential inclusions.
  • Understanding their solution existence is crucial for modeling complex systems.

Purpose of the Study:

  • To investigate the existence of solutions for two classes of fractional differential inclusions.
  • To analyze the existence and dimension of solution sets for fractional differential inclusions.

Main Methods:

  • Utilizing fixed-point theorems tailored for fractional calculus.
  • Applying techniques for hybrid fractional differential inclusions.

Main Results:

  • Demonstrated the existence of solutions for the considered fractional differential inclusions.
  • Provided an illustrative example to support the theoretical findings.
  • Characterized the dimension of the solution set for specific cases.

Conclusions:

  • The study confirms the existence of solutions for fractional hybrid differential inclusions.
  • The findings contribute to the theoretical framework of fractional differential equations and inclusions.