Exact solutions of fractional partial differential equation systems with conformable derivative

Abstract

Main goal of this paper is to have the new exact solutions of some fractional partial differential equation systems (FPDES) in conformable sense. The definition of conformable fractional derivative (CFD) is similar to the limit based definition of known derivative. This derivative obeys both rules which other popular derivatives do not satisfy such as derivative of the quotient of two functions, the derivative product of two functions, chain rule and etc. By using conformable derivative it is seen that the solution procedure for (PDES) is simpler and more efficient.1. The Riemann-Liouville derivative of a constant do not equal to zero (Caputo derivative satisfies).

Fuzzy Generalized Conformable Fractional Derivative

“…and multiplying by 1/ε, we have (ii) Let g(t) � e − t , so F(t) � (1, 2, 3)e − t and T q (e − t ) � − t 1− q e − t , then it is easy to see that T q (2) F(t) � − (1, 2, 3)t 1− q e − t , i.e., F q (2)…”

“…Fuzzy set theory is a powerful tool for modeling uncertainty and for processing vague or subjective information in mathematical models. eir main directions of development have been diversed, and its applications have been varied [1][2][3][4]. e derivative for fuzzy valued mappings was developed by Puri and Ralescu [5], which generalized and extended the concept of Hukuhara differentiability for set-valued mappings to the class of fuzzy mappings.…”

Existence and uniqueness of solutions to some classes of nonlocal semilinear conformable fractional differential or integrodifferential equations

“…It describes the most diminutive details of natural phenomena, which is better than using the integer calculus. For the history and more details about applications and significant results on fractional calculus, we refer to [4,6,9,12,21,[23][24][25][26]28].…”

Solving Higher-Order Fractional Differential Equations by the Fuzzy Generalized Conformable Derivatives

“…A fuzzy fractional differentiation and fuzzy integration operators have different kinds of definitions that we can mention, the fuzzy Riemann-Liouville definition [8,9], the fuzzy Caputo definition [9,10], and so on. Lately, Khalid et al [11] introduced a new simple definition of the fractional derivative named the conformable fractional derivative, which can redress shortcomings of the other definitions, and this new definition satisfies formulas of derivative of product and quotient of two functions [12,13]. Harir et al [14] introduced the fuzzy generalized conformable fractional derivative, which generalized and extended the concept of Hukuhara differentiability for set-valued mappings to the class of fuzzy mapping [15,16].…”