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Context 1
... this section, three solutions of space-time fractional SRLW equation from Table 2 and Table 3 in Table 2. Figure 1 illustrates this solution for −5 ≤ ξ ≤ 5 and 0 ≤ m ≤ 1. Besides, Figure 2 demonstrates 2D graph of the same solution for −5 ≤ ξ ≤ 5 and different m values; namely, the line with dots represents the solution when m = 0, the unitary line represents the solution when m = 0.5, the line with dashes represents the solution when m = 0.8 and the line with dotdashes represents the solution when m = 1. ...
Context 2
... this section, three solutions of space-time fractional SRLW equation from Table 2 and Table 3 in Table 2. Figure 1 illustrates this solution for −5 ≤ ξ ≤ 5 and 0 ≤ m ≤ 1. Besides, Figure 2 demonstrates 2D graph of the same solution for −5 ≤ ξ ≤ 5 and different m values; namely, the line with dots represents the solution when m = 0, the unitary line represents the solution when m = 0.5, the line with dashes represents the solution when m = 0.8 and the line with dotdashes represents the solution when m = 1. ...

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... In recent times the fractional order differential operators have made important contributions in the modeling of fractal and complex phenomena. In these models the JEFM have been successfully implemented bringing new families of analytical solutions [59][60][61][62][63][64][65][66][67][68][69][70][71][72][73]. ...
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Chapter
As fractional operators are nonlocal, they can describe several natural phenomena in a more systematic and applicable way. Fractional calculus has many applications to complex real‐world problems, and its equations describe the behavior of many mathematical models in a better way. Engineers, mathematicians, scientists, and researchers dealing with real‐life phenomena may benefit significantly from fractional derivatives and integrals. This chapter summarizes recent investigations illustrating the depth and breadth of ongoing research in fractional calculus and its corresponding applications. Variety of physical phenomena such as fluid dynamics, quantum mechanics, electricity, ecological systems, and various other models are governed by fractional‐order partial differential equations (PDEs). As a result, all traditional and recently developed methods for solving fractional‐order PDEs and their implementations have become increasingly important. Thus, numerical, analytical, and semi‐analytical methods for handling fractional‐order complex phenomena have also been discussed.